Which operation converts \(3.6\,\text{m}\) to centimeters: multiply by \(100\) or divide by \(100\)? Then give the converted measurement.

The number line is measured in centimeters. Which marker shows the same length as \(1.2\,\text{m}\)?

The number-line scale is in centimeters. How many meters long is the marked segment?

Evaluate \(12\,\text{cm}\div3\,\text{cm}\). Does the answer have a length unit? Explain.

A sporting goods store measures the mass and diameter of several balls. Convert each mass from kilograms (\(\text{kg}\)) to grams (\(\text{g}\)) and each diameter from meters (\(\text{m}\)) to centimeters (\(\text{cm}\)). <table> <tr> <th>Ball</th> <th>Basketball</th> <th>Soccer ball</th> <th>Handball</th> <th>Tennis ball</th> </tr> <tr> <th>Mass</th> <td>\(0.625\,\text{kg}\)</td> <td>\(0.430\,\text{kg}\)</td> <td>\(0.375\,\text{kg}\)</td> <td>\(0.058\,\text{kg}\)</td> </tr> <tr> <th>Diameter</th> <td>\(0.24\,\text{m}\)</td> <td>\(0.22\,\text{m}\)</td> <td>\(0.19\,\text{m}\)</td> <td>\(0.07\,\text{m}\)</td> </tr> </table>

Convert each mass to grams (\(\text{g}\)): a) \(1.500\,\text{kg}\) b) \(0.725\,\text{kg}\) c) \(0.040\,\text{kg}\) d) \(3.005\,\text{kg}\)

Write each mass as a decimal number of kilograms, \(\text{kg}\). Use three decimal places to show grams. a) \(3250\,\text{g}\) b) \(805\,\text{g}\) c) \(12{,}004\,\text{g}\)

Write each mixed-unit mass as a decimal number of kilograms. a) \(5\,\text{kg}\ 70\,\text{g}\) b) \(18\,\text{kg}\ 205\,\text{g}\) c) \(0\,\text{kg}\ 9\,\text{g}\)

Complete the table. <table> <tr> <td>Fraction form</td> <td>Mass in grams</td> <td>Decimal form in kilograms</td> </tr> <tr> <td>\(\frac{1}{2}\,\text{kg}\)</td> <td>\(500\,\text{g}\)</td> <td>\(0.500\,\text{kg}\)</td> </tr> <tr> <td>\(\frac{1}{4}\,\text{kg}\)</td> <td>\(\square\)</td> <td>\(\square\)</td> </tr> <tr> <td>\(\frac{3}{4}\,\text{kg}\)</td> <td>\(\square\)</td> <td>\(\square\)</td> </tr> </table>

Fill in each missing length unit. Use millimeters, centimeters, meters, or kilometers. a) \(13\,\text{m}=13000\,\square\) b) \(5\,\text{m}=500\,\square\) c) \(8000\,\text{m}=8\,\square\) d) \(4\,\square=4000\,\text{mm}\)

Convert each measurement to the indicated unit. Write the missing numerical value. a) \(12\,\text{m}=\square\,\text{cm}\) b) \(900\,\text{cm}=\square\,\text{m}\) c) \(7\,\text{km}=\square\,\text{m}\) d) \(250\,\text{mm}=\square\,\text{cm}\)

Write \(<\), \(>\), or \(=\) in each blank. a) \(400\,\text{m}\ \square\ 4\,\text{km}\) b) \(300\,\text{cm}\ \square\ 3\,\text{m}\) c) \(25\,\text{cm}\ \square\ 250\,\text{mm}\) d) \(5\,\text{m}\ \square\ 550\,\text{cm}\)

Convert each length to the unit in parentheses. a) \(5200\,\text{mm}\) (centimeters) b) \(14\,\text{m}\ 5\,\text{cm}\) (centimeters) c) \(3200\,\text{cm}\) (meters) d) \(9\,\text{km}\ 75\,\text{m}\) (meters) e) \(63\,\text{cm}\) (millimeters)

Which measurements describe the same length? Find the three matching pairs. A: \(400\,\text{cm}\) B: \(40\,\text{m}\) C: \(40\,\text{cm}\) D: \(400\,\text{mm}\) E: \(4000\,\text{mm}\) F: \(4000\,\text{cm}\)

Julia says, “\(0.8\,\text{m}\) is shorter than \(75\,\text{cm}\) because \(0.8\) is less than \(75\).” Is Julia correct? Convert the measurements to the same unit and explain.

Fill in each missing number or unit so the equation is true. a) \(4.2\,\text{m}=4\,\text{m}\ \square\,\text{cm}\) b) \(520\,\text{mm}=52\,\square\) c) \(3\,\text{cm}\ 4\,\text{mm}=\square\,\text{mm}\) d) \(0.8\,\text{m}=\square\,\text{cm}\)

Fill in each missing value or unit. a) \(12.5\,\text{km}=12\,\text{km}\ \square\,\text{m}\) b) \(705\,\text{cm}=7\,\square\ 5\,\text{cm}\) c) \(2\,\text{m}\ 3\,\text{cm}=203\,\square\) d) \(1500\,\text{m}=1.5\,\square\)

Fill in each missing number or unit. a) \(8\,\text{cm}\ 9\,\text{mm}=\square\,\text{mm}\) b) \(1.03\,\text{m}=1\,\text{m}\ 3\,\square\) c) \(600\,\text{cm}=\square\,\text{m}\) d) \(4500\,\text{m}=\square\,\text{km}\)

Convert each length to the specified smaller unit. a) \(4.2\,\text{km}\) to meters b) \(17\,\text{m}\) to centimeters c) \(0.5\,\text{m}\) to centimeters d) \(240\,\text{cm}\) to millimeters

Write each length using the indicated mixed units. a) Write \(842\,\text{cm}\) in meters and centimeters. b) Write \(305\,\text{cm}\) in meters and centimeters. c) Write \(2007\,\text{mm}\) in meters and millimeters. d) Write \(95\,\text{mm}\) in centimeters and millimeters.

Pair the measurements that have the same weight. Which measurement has no partner? Explain by converting between pounds and ounces. \(7.5\,\text{lb}\); \(72\,\text{oz}\); \(5\,\text{lb}\); \(120\,\text{oz}\); \(80\,\text{oz}\)

Convert each length to the unit in parentheses. a) \(7.2\,\text{m}\) (centimeters) b) \(540\,\text{cm}\) (meters) c) \(20\,\text{cm}\ 8\,\text{mm}\) (millimeters) d) \(9000\,\text{mm}\) (centimeters)

Write \(<\), \(>\), or \(=\) in each box. a) \(230\,\text{mm}\ \square\ 2.3\,\text{cm}\) b) \(1.5\,\text{m}\ \square\ 150\,\text{cm}\) c) \(47\,\text{cm}\ \square\ 407\,\text{mm}\) d) \(0.8\,\text{km}\ \square\ 800\,\text{m}\)

Order the lengths from least to greatest using \(<\). \(75\,\text{cm}\); \(0.8\,\text{m}\); \(720\,\text{mm}\); \(71\,\text{cm}\)

Convert \(4\,\text{kg}\ 20\,\text{g}\), \(420\,\text{g}\), \(4002\,\text{g}\), and \(0.42\,\text{kg}\) to grams. Then order the original measurements from least to greatest.

Convert \(5\,\text{m}\ 8\,\text{cm}\), \(580\,\text{cm}\), \(508\,\text{mm}\), and \(5.8\,\text{m}\) to centimeters. Then order the original measurements from greatest to least.

Calculate each result and write it using mixed units of meters and centimeters. a) \(86\,\text{cm} + 45\,\text{cm}\) b) \(264\,\text{cm} - 0.84\,\text{m}\)

Convert each mass to the unit in parentheses. a) \(8\,\text{kg}\ 150\,\text{g}\) (grams) b) \(450\,\text{g}\) (kilograms) c) \(1.5\,\text{g}\) (milligrams) d) \(7200\,\text{mg}\) (grams)

Convert each length to the unit in parentheses. a) \(2.75\,\text{km}\) (meters) b) \(80\,\text{cm}\) (meters) c) \(4\,\text{m}\ 3\,\text{cm}\) (centimeters) d) \(5\,\text{cm}\) (millimeters)

Fill in each missing unit or numerical value. a) \(5600\,\text{g}=5.6\,\square\) b) \(12\,\text{cm}=\square\,\text{mm}\) c) \(0.25\,\text{km}=250\,\square\) d) \(35\,\text{g}=\square\,\text{mg}\)

Rewrite each decimal mass without a decimal, using mixed units when needed. a) \(5.4\,\text{kg}\) b) \(0.025\,\text{kg}\) c) \(10.705\,\text{kg}\) d) \(0.008\,\text{g}\)

Complete the table for each mass. <table> <tr> <td>Mass in grams</td> <td>\(7040\,\text{g}\)</td> <td></td> <td></td> <td>\(12{,}300\,\text{g}\)</td> </tr> <tr> <td>Mass in kilograms and grams</td> <td></td> <td>\(5\,\text{kg}\ 8\,\text{g}\)</td> <td></td> <td></td> </tr> <tr> <td>Decimal mass in kilograms</td> <td></td> <td></td> <td>\(0.015\,\text{kg}\)</td> <td></td> </tr> </table>

Write \(<\), \(>\), or \(=\) in each box. Convert to a common unit first. a) \(2\,\text{km}\ 50\,\text{m}\ \square\ 2.5\,\text{km}\) b) \(0.08\,\text{km}\ \square\ 80\,\text{m}\) c) \(1205\,\text{m}\ \square\ 1\,\text{km}\ 25\,\text{m}\) d) \(3.007\,\text{km}\ \square\ 3007\,\text{m}\)

Order the lengths from least to greatest. \(40.5\,\text{cm}\); \(4005\,\text{mm}\); \(4\,\text{m}\ 5\,\text{cm}\); \(0.004\,\text{km}\); \(420\,\text{cm}\); \(4.5\,\text{m}\)

Order the masses from least to greatest. \(850\,\text{g}\); \(0.805\,\text{kg}\); \(8\,\text{kg}\); \(8050\,\text{g}\); \(8.5\,\text{kg}\); \(85\,\text{g}\)

Convert each mass to the unit in parentheses. a) \(75\,\text{g}\) (kilograms) b) \(4000\,\text{g}\) (kilograms) c) \(850\,\text{g}\) (kilograms) d) \(1.2\,\text{g}\) (milligrams)

Write \(<\), \(>\), or \(=\) in each blank. a) \(0.3\,\text{kg}\ \square\ 30\,\text{g}\) b) \(\frac{1}{2}\,\text{kg}\ \square\ 500\,\text{g}\) c) \(1200\,\text{mg}\ \square\ 1.2\,\text{g}\) d) \(0.07\,\text{kg}\ \square\ 700\,\text{g}\)

A storage bin contains \(9\,\text{lb}\) of coffee beans. The beans are packed into \(8\)-ounce bags. How many full bags can be filled? Use \(1\,\text{lb} = 16\,\text{oz}\).

Convert each time measurement to the unit in parentheses. a) \(8\,\text{h}\) (minutes) b) \(360\,\text{s}\) (minutes) c) \(3\,\text{days}\) (hours) d) \(540\,\text{min}\) (hours)

Write each time interval entirely in the smaller unit shown. a) \(4\,\text{min}\ 12\,\text{s}\) b) \(2\,\text{h}\ 45\,\text{min}\) c) \(1\,\text{day}\ 10\,\text{h}\)

Write each mixed measurement entirely in the smaller unit. a) \(2\,\text{kg}\ 450\,\text{g}\) b) \(15\,\text{kg}\ 30\,\text{g}\) c) \(9\,\text{km}\ 75\,\text{m}\) d) \(4\,\text{m}\ 25\,\text{cm}\)

An intercity train trip takes exactly \(2\,\text{h}\ 17\,\text{min}\). Write the entire travel time in minutes.

Write each time measurement using mixed units. a) \(450\,\text{s}\) b) \(190\,\text{min}\) c) \(2.5\,\text{h}\) d) \(62\,\text{h}\)

Which time measurements are equivalent? Match each letter to a number. A: \(130\,\text{s}\) B: \(2\,\text{h}\ 15\,\text{min}\) C: \(85\,\text{min}\) 1: \(135\,\text{min}\) 2: \(2\,\text{min}\ 10\,\text{s}\) 3: \(1\,\text{h}\ 25\,\text{min}\)

Convert each measurement to the unit in parentheses. Use decimals when needed. a) \(45\,\text{mm}\) (centimeters); \(0.32\,\text{m}\) (centimeters); \(1\,\text{m}\ 5\,\text{cm}\) (centimeters) b) \(2700\,\text{g}\) (kilograms); \(4000\,\text{g}\) (kilograms); \(15\,\text{kg}\ 500\,\text{g}\) (kilograms)

Write \(<\), \(>\), or \(=\) in each blank. Convert one measurement to the other unit before comparing. a) \(2500\,\text{m}\ \square\ 2.5\,\text{km}\) b) \(75\,\text{min}\ \square\ 1.5\,\text{h}\) c) \(300\,\text{mg}\ \square\ 0.3\,\text{g}\) d) \(1\,\text{kg}\ 50\,\text{g}\ \square\ 1500\,\text{g}\)

Fill in each missing number or unit. a) \(4\,\text{km}\ 12\,\text{m}=\square\,\text{m}\) b) \(7\,\text{kg}\ \square\,\text{g}=7005\,\text{g}\) c) \(2\,\text{m}\ 3\,\text{cm}\ 5\,\text{mm}=\square\,\text{mm}\) d) \(12\,\text{kg}\ 80\,\text{g}=12{,}080\,\square\)

Measurements can be written as decimals or with mixed units. Fill in each blank. a) \(5.4\,\text{m}=5\,\text{m}\ \square\,\text{cm}\) b) \(3.02\,\text{kg}=3\,\text{kg}\ \square\,\text{g}\) c) \(0.75\,\text{m}=\square\,\text{cm}\) d) \(8.1\,\text{cm}=8\,\text{cm}\ \square\,\text{mm}\)

Find each missing value. a) \(3\,\text{days}\ 4\,\text{h}=\square\,\text{h}\) b) \(2\,\text{h}\ 15\,\text{min}=\square\,\text{min}\) c) \(\square\,\text{h}\ 20\,\text{min}=200\,\text{min}\) d) \(1.5\,\text{h}=\square\,\text{min}\)

Write \(<\), \(>\), or \(=\) to make each statement true. a) \(2\,\text{km}\ 50\,\text{m}\ \square\ 2005\,\text{m}\) b) \(0.12\,\text{m}\ \square\ 12\,\text{cm}\) c) \(60\,\text{mm}\ \square\ 0.06\,\text{m}\)

Amira writes \(6.5\,\text{m} + 250\,\text{cm} = 256.5\,\text{m}\). Explain the error and find the correct result in meters.

Rewrite each measurement without a decimal, using mixed units when needed. a) \(12.050\,\text{km}\) b) \(4.07\,\text{m}\) c) \(0.625\,\text{kg}\) d) \(30.2\,\text{kg}\)

Complete the missing equivalent forms. a) \(6.305\,\text{km}=\square\,\text{km}\ \square\,\text{m}=\square\,\text{m}\) b) \(15\,\text{kg}\ 400\,\text{g}=\square\,\text{kg}=\square\,\text{g}\) c) \(0.08\,\text{m}=\square\,\text{cm}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(12\,\text{cm}\ 5\,\text{mm}\ \square\ 12.05\,\text{cm}\) b) \(3\,\text{km}\ 20\,\text{m}\ \square\ 3.2\,\text{km}\) c) \(450\,\text{m}\ \square\ 0.45\,\text{km}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(4\,\text{kg}\ 50\,\text{g}\ \square\ 4.5\,\text{kg}\) b) \(0.8\,\text{kg}\ \square\ 80\,\text{g}\) c) \(2500\,\text{mg}\ \square\ 2.5\,\text{g}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(1\,\text{h}\ 45\,\text{min}\ \square\ 100\,\text{min}\) b) \(3\,\text{min}\ 12\,\text{s}\ \square\ 192\,\text{s}\) c) \(2\,\text{days}\ 4\,\text{h}\ \square\ 50\,\text{h}\)

Write each length as a decimal in the unit in parentheses. a) \(6\,\text{m}\ 30\,\text{cm}\) (meters) b) \(25\,\text{cm}\) (meters) c) \(8\,\text{km}\ 75\,\text{m}\) (kilometers)

Convert each measurement to the unit in parentheses. a) \(34\,\text{m}\) (centimeters) b) \(8000\,\text{g}\) (kilograms) c) \(4000\,\text{g}\) (kilograms) d) \(120\,\text{min}\) (hours) e) \(70\,\text{cm}\) (meters)

Find each missing value. a) \(2.5\,\text{kg}=\square\,\text{g}\) b) \(3\,\text{h}\ 15\,\text{min}=\square\,\text{min}\) c) \(12\,\text{cm}\ 5\,\text{mm}=\square\,\text{mm}\) d) \(1.25\,\text{m}=\square\,\text{cm}\)

Convert each fractional measurement to the smaller unit. a) How many grams are in one-half kilogram? b) How many centimeters are in one-fifth meter? c) How many grams are in one-tenth kilogram?

How much time remains in a \(24\)-hour day after \(5\,\text{h}\ 18\,\text{min}\) have passed?

The number-line scale is in grams, and marker P shows a package's mass. Which is greater: the package at P or \(0.65\,\text{kg}\)? Explain.

A ribbon is \(2\,\text{m}\) long. It is cut into pieces that are each \(25\,\text{cm}\) long. How many pieces are made?

\(6\,\text{lb}\,12\,\text{oz}\) of candy is shared equally among \(18\) children. How many ounces does each child receive? Use \(1\,\text{lb} = 16\,\text{oz}\).

Compare the values. Insert \(<\), \(>\), or \(=\). First evaluate each quotient and express both sides in the same unit. a) \(5\,\text{m}\div4\ \square\ 120\,\text{cm}\) b) \(1\,\text{kg}\div8\ \square\ 125\,\text{g}\) c) \(7\,\text{km}\div10\ \square\ 0.75\,\text{km}\)

Calculate each sum. Write each answer as a fraction in simplest form using the larger unit. a) \(25\,\text{cm} + \frac{1}{2}\,\text{m}\) b) \(150\,\text{g} + \frac{3}{4}\,\text{kg}\) c) \(10\,\text{min} + \frac{1}{6}\,\text{h}\)

Two packages are weighed. Package A weighs \(39\,\text{oz}\), and Package B weighs \(2.55\,\text{lb}\). a) What is each weight rounded to the nearest whole pound? b) Are the rounded weights different? Explain why this happens even though the actual weights are close.

Three friends compare their routes to school. Lucas walks \(\frac{3}{4}\) mile, Mia walks \(1200\) yards, and Ben walks \(\frac{4}{5}\) mile. Order the routes from shortest to longest.

Four packages have weights written in different forms. - Package A: \(40\,\text{oz}\) - Package B: \(2\frac{2}{5}\,\text{lb}\) - Package C: \(2.05\,\text{lb}\) - Package D: \(2\,\text{lb}\ 0.8\,\text{oz}\) a) Convert every weight to pounds. b) Order the packages from lightest to heaviest.

Four students compare the weights of their lunch bags. - Alex: \(3.45\,\text{lb}\) - Mia: \(48.8\,\text{oz}\) - Jordan: \(3.6\,\text{lb}\) - Sam: \(3\frac{1}{2}\,\text{lb}\) Order the lunch bags from heaviest to lightest. Briefly explain why Mia’s bag is not the heaviest even though \(48.8\) is the largest numerical value shown.

A construction site receives these materials: - Sand: \(0.8\,\text{ton}\) - Gravel: \(1700\,\text{lb}\) - Cement: \(0.09\,\text{ton}\) - Water: \(240\,\text{lb}\) a) Find the total weight in tons. b) Which material has the second-greatest weight? Use \(1\,\text{ton} = 2000\,\text{lb}\).

A shelf can safely hold at most \(30\,\text{lb}\). Four packages on the shelf weigh \(7 \frac{1}{2}\,\text{lb}\), \(4 \frac{1}{4}\,\text{lb}\), \(9 \frac{3}{4}\,\text{lb}\), and \(3 \frac{1}{2}\,\text{lb}\). Can another package weighing \(72\,\text{oz}\) be added safely? Explain.

A flatbed truck can carry at most \(12 \frac{1}{8}\) tons. It is already carrying loads of \(2 \frac{3}{8}\) tons, \(3 \frac{1}{2}\) tons, \(1 \frac{3}{4}\) tons, and \(2 \frac{1}{2}\) tons. A pallet weighing \(4200\,\text{lb}\) is ready to be added. Find the truck's remaining capacity and decide whether the pallet can be loaded safely.

For a simplified scale comparison, take a red blood cell diameter as \(0.008\,\text{mm}\) and a small blood vessel's inside diameter as \(0.032\,\text{mm}\). a) Convert both measurements to micrometers \((\mu\text{m})\). Use \(1\,\text{mm}=1000\,\mu\text{m}\). b) How many times as large is the blood vessel's diameter as the blood cell's diameter?

In a particle-size model, Particle A has diameter \(0.024\,\text{mm}\), Particle B has diameter \(0.006\,\text{mm}\), and Particle C has diameter \(0.3\,\mu\text{m}\). Use \(1\,\text{mm}=1000\,\mu\text{m}\). a) How many Particle B diameters placed end to end equal one Particle A diameter? b) How many Particle C diameters placed end to end equal one Particle B diameter?

A workshop receives a box containing \(400\) identical metal washers. The full box weighs \(1.58\,\text{kg}\), and the empty box weighs \(140\,\text{g}\). a) Find the weight of one washer in grams. b) How many grams do \(10\) washers weigh?

A room is \(12.5\,\text{ft}\) long. a) Find the room length in inches. b) A hallway runner is \(12\,\text{ft}\ 8\,\text{in}\) long. Will it fit lengthwise in the room? Justify your answer by comparing the lengths in the same unit.

A case contains \(12\) identical juice pouches. The full case weighs \(2.7\,\text{kg}\), and the empty cardboard case weighs \(60\,\text{g}\). Find the weight of one juice pouch in grams.

A bakery orders flour in bags that each have a mass of \(25\,\text{kg}\). Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) How many bags have a total mass of exactly \(1\) metric ton? b) What is the total mass of \(10\) bags in grams?

Darius attends school on \(180\) days each year. His one-way walk to school is \(950\,\text{m}\). How many kilometers does he walk altogether traveling to and from school during the year?

Two ropes are cut into equal-length pieces. Rope A is \(25.68\,\text{m}\) long and is cut into \(8\) equal pieces. Rope B is \(19.26\,\text{m}\) long and is cut into \(6\) equal pieces. Find the length of one piece from each rope in centimeters. Which rope makes longer pieces, or are the pieces equal in length?

A bakery uses exactly \(500\,\text{g}\) of butter for one sheet cake. A bulk box contains \(10\,\text{kg}\) of butter. a) How many sheet cakes can be made with one box? b) The bakery uses \(12\) boxes in one week. How many sheet cakes are made that week?

Nora records the time she spends on homework and studying each school day: <table> <tr><td>Math</td><td>\(25\,\text{minutes}\)</td></tr> <tr><td>Language arts</td><td>\(25\,\text{minutes}\)</td></tr> <tr><td>Science</td><td>\(15\,\text{minutes}\)</td></tr> <tr><td>Spanish</td><td>\(10\,\text{minutes}\)</td></tr> <tr><td>Independent reading</td><td>\(15\,\text{minutes}\)</td></tr> </table> a) Find the total study time per day in minutes. b) Find the total study time in a \(5\)-day school week. Give the answer in hours and minutes. c) A school year has \(40\) school weeks. Find the total study time for the school year in hours.

An elephant in a national park lives to be \(70\) years old. Determine whether the elephant has lived more than \(600{,}000\) hours by its 70th birthday. Assume every year has exactly \(365\) days.

A high-speed train travels \(2850\,\text{km}\) on its route. Priya claims that this distance is greater than \(250\) million centimeters. Is Priya correct? Show how you know.

A recycling facility processes \(3500\,\text{kg}\) of material each day. Does it process more than \(1250\) metric tons in \(365\) days? Use \(1\,\text{metric ton}=1000\,\text{kg}\). Show how you know.

Ethan takes exactly \(2000\) steps on a walk. His average step length is \(60\,\text{cm}\). Find the total distance first in centimeters, then convert it to meters and kilometers.

Nadia and Tom each walk exactly \(400\,\text{m}\). Nadia’s average step length is \(50\,\text{cm}\), and Tom’s average step length is \(80\,\text{cm}\). How many steps does each person take?

A hiking trail is \(3\,\text{km}\) long. Mrs. Smith estimates that she takes \(4000\) steps to complete the trail. a) If her estimate is exact, what is her average step length in centimeters? b) Her small dog travels the same distance using exactly twice as many steps. How many steps does the dog take, and what is the dog’s average step length?

Order the lengths from least to greatest using \(<\). First convert every measurement to centimeters. \(30\,\text{cm}\); \(250\,\text{mm}\); \(0.5\,\text{m}\); \(12\,\text{cm}\); \(0.002\,\text{km}\)

A stack of \(100\) sheets of printer paper is exactly \(1\,\text{cm}\) high. a) How thick is one sheet of paper in millimeters? b) How many sheets are in a stack that is \(20\,\text{cm}\) high? c) Elena claims, “A package of \(500\) sheets is \(25\,\text{cm}\) high.” Use a calculation to decide whether the claim is reasonable.

Fill in each missing number or unit so the equation is true. a) \(7\,\text{m}\ 4\,\text{cm}=\square\,\text{cm}\) b) \(85\,\text{mm}=8\,\text{cm}\ \square\,\text{mm}\) c) \(1200\,\text{m}=1\,\text{km}\ \square\,\text{m}\) d) \(4500\,\text{cm}=45\,\square\) e) \(3\,\text{cm}\ 2\,\text{mm}=\square\,\text{mm}\)

Four lengths are shown. A: \(4.6\,\text{m}\) B: \(540\,\text{cm}\) C: \(0.006\,\text{km}\) D: \(460\,\text{mm}\) Which two measurements have a combined length of exactly \(10\,\text{m}\)? Justify your choice by converting all four measurements to meters.

Complete the conversion chain. \(0.05\,\text{km}=\square\,\text{m}=\square\,\text{cm}=\square\,\text{mm}\)

Write each length without a decimal. For a), b), and d), use only meters and centimeters. For c), use only kilometers and meters. Omit a larger unit when its amount is zero. a) \(7.2\,\text{m}\) b) \(14.06\,\text{m}\) c) \(5.125\,\text{km}\) d) \(0.68\,\text{m}\)

Rewrite each length without a decimal using the indicated units. Omit any unit whose amount is zero. a) Write \(10.04\,\text{km}\) in kilometers and meters. b) Write \(2.5\,\text{cm}\) in centimeters and millimeters. c) Write \(4070\,\text{mm}\) in meters and centimeters. d) Write \(0.009\,\text{m}\) in millimeters.

Evaluate each expression. First convert every measurement to the smallest unit used in that part. a) \(12\,\text{m}\ 8\,\text{cm}+30\,\text{cm}\) b) \(2\,\text{km}\ 45\,\text{m}-120\,\text{m}\) c) \((40\,\text{cm}\ 6\,\text{mm})\times 5\)

For each pair, determine which length is longer and by how much. Give each difference in centimeters. a) \(2.8\,\text{m}\) and \(265\,\text{cm}\) b) \(0.004\,\text{km}\) and \(390\,\text{cm}\)

Write \(<\), \(>\), or \(=\) in each box. a) \(6\,\text{m}\ 50\,\text{cm}\ \square\ 6.05\,\text{m}\) b) \(1200\,\text{mm}\ \square\ 120\,\text{cm}\) c) \(0.04\,\text{km}\ \square\ 400\,\text{m}\) d) \(9\,\text{cm}\ 2\,\text{mm}\ \square\ 9.2\,\text{cm}\)

A package currently weighs \(16\,\text{lb}\,7\,\text{oz}\). Two more items are added, and each weighs \(1\,\text{lb}\,14\,\text{oz}\). Is the package now heavier or lighter than \(20\,\text{lb}\)? Use \(1\,\text{lb} = 16\,\text{oz}\).

A rope is \(12.4\,\text{m}\) long. First, a \(3.85\,\text{m}\) piece is cut off. Then a piece measuring \(4\,\text{m}\,60\,\text{cm}\) is cut off. Is the remaining piece longer or shorter than \(4\,\text{m}\)?

Find the remaining length and write the result as a decimal number of meters: \(3.5\,\text{m} - 120\,\text{cm} - 450\,\text{mm}\).

Calculate and write the result as a decimal number of kilograms: \(1.25\,\text{kg} + 850\,\text{g} - 0.4\,\text{kg} - 325\,\text{g}\).

Convert all addends to grams, write the sum as a product, and calculate: \(250\,\text{g} + 250\,\text{g} + 250{,}000\,\text{mg} + 0.25\,\text{kg} + 250\,\text{g}\).

Write the sum as a product, calculate its value, and give the result in meters: \(45\,\text{cm} + 0.45\,\text{m} + 450\,\text{mm} + 45\,\text{cm}\).

Calculate efficiently and give the result in meters and centimeters: \(6\,\text{m}\,80\,\text{cm} + 14\,\text{m}\,36\,\text{cm} + 20\,\text{cm} + 65\,\text{cm}\).

Calculate each result and write it in mixed units of meters and centimeters. a) \(18\,\text{m}\,42\,\text{cm} - 5.9\,\text{m}\) b) \(2\,\text{m}\,5\,\text{cm} + 740\,\text{mm} + 30\,\text{cm}\)

Calculate each result and briefly describe what happens to the units. a) \(4.2\,\text{m} \div 7\) b) \(4.2\,\text{m} \div 30\,\text{cm}\) c) \(4.2\,\text{m} - 50\,\text{cm}\) What general rule can you state about dividing one measurement by another measurement of the same kind, as in part b)?

A ribbon is \(2.4\,\text{m}\) long. a) The ribbon is cut into \(12\) equal pieces. Find the length of each piece in centimeters and explain your method. b) How many \(15\,\text{cm}\) pieces can be cut from the entire ribbon? c) Give another everyday example in which dividing one length by another length gives a count.

A class hikes for four days. The distances are \(12\,\text{km}\,450\,\text{m}\), \(15\,\text{km}\,720\,\text{m}\), \(8\,\text{km}\,900\,\text{m}\), and \(11\,\text{km}\,130\,\text{m}\). How far does the class hike altogether? Give the result in kilometers and meters.

A courier records four driving segments during the morning. <table> <tr><th>Segment</th><th>Distance</th></tr> <tr><td>Warehouse to Stop A</td><td>\(8\,\text{mi}\,1200\,\text{ft}\)</td></tr> <tr><td>Stop A to Stop B</td><td>\(2600\,\text{ft}\)</td></tr> <tr><td>Stop B to Stop C</td><td>\(2\,\text{mi}\,375\,\text{ft}\)</td></tr> <tr><td>Stop C back to the warehouse</td><td>\(1800\,\text{ft}\)</td></tr> </table> Find the total distance driven. Give the result in miles and feet. Use \(1\,\text{mi} = 5280\,\text{ft}\).

A truck carries two heavy crates. The first weighs \(2\,\text{tons}\,900\,\text{lb}\), and the second weighs \(1750\,\text{lb}\). First estimate the total weight. Then find the exact total in pounds. Use \(1\,\text{ton} = 2000\,\text{lb}\).

A garden fence requires \(12\) rolls of wire. Each roll is \(15\,\text{ft}\,11\,\text{in}\) long. First estimate the total length. Then find the exact total in feet and inches.

A ribbon \(15\,\text{ft}\,6\,\text{in}\) long is cut into \(6\) equal pieces. First estimate the length of one piece. Then find the exact length.

Evaluate and write the result as a decimal number of kilograms: \(12.5\,\text{kg} - (4\,\text{kg}\,250\,\text{g} - 1\,\text{kg}\,75\,\text{g})\).

Leo wants to hang a picture. The hook is \(7\,\text{ft}\,1\,\text{in}\) above the floor. Leo is \(5\,\text{ft}\,2\,\text{in}\) tall and can reach \(10\,\text{in}\) above the top of his head. He stands on a \(16\)-inch stool. Can Leo reach the hook?

Maya wants to touch a ceiling that is \(8\,\text{ft}\,2\,\text{in}\) high. She is \(4\,\text{ft}\,10\,\text{in}\) tall and can reach \(13\,\text{in}\) above the top of her head. Each ladder step raises her \(8\,\text{in}\). What is the lowest step Maya must stand on to reach the ceiling with her fingertips?

An apple hangs from a branch \(9\,\text{ft}\,4\,\text{in}\) above the ground. Tom is \(5\,\text{ft}\,1\,\text{in}\) tall, can reach \(14\,\text{in}\) above his head, and has a \(24\)-inch stool. Marie is \(5\,\text{ft}\,4\,\text{in}\) tall, can reach \(15\,\text{in}\) above her head, and has a \(36\)-inch step ladder. Who can reach the apple? Find each person’s maximum reach.

Estimate first, then evaluate exactly: \((15\,\text{m} - 700\,\text{cm}) \times 12 + 400\,\text{cm} \times 5\).

Estimate first, then evaluate exactly: \((2\,\text{km} + 400\,\text{m}) \div 8 + 70\,\text{m} \times 6\).

Estimate first, then evaluate exactly: \(25\,\text{cm} \times 4 + (1.8\,\text{m} - 60\,\text{cm}) \div 3\).

During a school fundraiser walk, Team A travels \(6.2\,\text{km}\). Team B travels \(450\,\text{m}\) farther than Team A. Team C travels half as far as Team A. Give all three distances in kilometers.

Three crates have different masses. Find the missing masses for Crates 2 and 3 in grams. <table> <tr><th>Crate</th><th>Mass</th></tr> <tr><td>Crate 1</td><td>\(3.6\,\text{kg}\)</td></tr> <tr><td>Crate 2</td><td>\(150\,\text{g}\) less than Crate 1</td></tr> <tr><td>Crate 3</td><td>Half the mass of Crate 1</td></tr> </table>

A hiking trail is \(15\,\text{km}\,600\,\text{m}\) long and is divided into equal sections of \(1300\,\text{m}\). a) Determine whether the trail has \(8\), \(10\), or \(12\) sections. b) A hiker’s average step length is \(65\,\text{cm}\). About how many steps are needed for one section?

Kofi converted each mass to mixed units. Check each result. Identify the incorrect results and write the correct conversion. a) \(4.5\,\text{kg}=4\,\text{kg}\ 5\,\text{g}\) b) \(0.025\,\text{kg}=25\,\text{g}\) c) \(7.08\,\text{g}=7\,\text{g}\ 80\,\text{mg}\) d) \(1.3\,\text{kg}=1\,\text{kg}\ 3\,\text{g}\)

Mei wrote three chains of equivalent masses, but each row contains exactly one error. Find and correct the incorrect measurement. a) \(4500\,\text{g}=4\,\text{kg}\ 500\,\text{g}=45\,\text{kg}\) b) \(3\,\text{kg}\ 20\,\text{g}=3020\,\text{g}=3.2\,\text{kg}\) c) \(6\,\text{kg}\ 4\,\text{g}=6.004\,\text{kg}=604\,\text{g}\)

Calculate and give each result in kilograms. Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) \(14.8\,\text{kg}+350\,\text{g}\) b) \(2.05\,\text{metric tons}-80\,\text{kg}\) c) \(1.2\,\text{kg}+400\,\text{g}+0.85\,\text{kg}\)

Calculate and give each result in kilograms. Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) \(12\frac{1}{2}\,\text{kg}-4.25\,\text{kg}-750\,\text{g}\) b) \(3\,\text{metric tons}-(1200\,\text{kg}+400\,\text{kg}\times2)\)

Calculate and give each final result in kilograms. Use \(1\,\text{metric ton}=1000\,\text{kg}\). a) \(5.4\,\text{kg}+(8.2\,\text{kg}-6500\,\text{g})\times5\) b) \(0.6\,\text{metric ton}-150\frac{1}{2}\,\text{kg}-4500\,\text{g}\)

Evaluate: \(12\,\text{kg}\,750\,\text{g} \div 250\,\text{g} + 8\,\text{g}\,40\,\text{mg} \div 20\,\text{mg} - 15\).

Evaluate: \(15\,\text{kg} - (3\,\text{kg}\,450\,\text{g} + 720\,\text{g} \times 5)\).

Convert each mass to the unit in parentheses. Pay attention to fractions and mixed units. a) \(\frac{3}{4}\,\text{kg}\) (grams) b) \(5\,\text{kg}\ 20\,\text{g}\) (kilograms) c) \(12\,\text{kg}\ 500\,\text{g}\) (kilograms) d) \(2\,\text{kg}\ \frac{1}{2}\,\text{g}\) (grams)

A charter bus is preparing for a class trip with \(48\) students and \(2\) teachers. Use an average person weight of \(120\,\text{lb}\). Each person may also bring a suitcase weighing up to \(30\,\text{lb}\) and a carry-on weighing \(10\,\text{lb}\). a) If everyone uses the full luggage allowance, what total weight do the people and luggage add to the bus? b) The unloaded bus weighs \(13\) tons. What is the fully loaded bus’s total weight in tons? Use \(1\,\text{ton} = 2000\,\text{lb}\). c) Ten people each have a suitcase that is \(4\,\text{lb}\) over the limit. By how many pounds does this increase the answer to part a)?

Evaluate and give the result in kilograms: \((1\,\text{kg}\,450\,\text{g} + 850\,\text{g} - 700\,\text{g}) \times 6\).

Evaluate: \(7.2\,\text{kg} - (2\frac{1}{4}\,\text{kg} + 1\,\text{kg}\,850\,\text{g} + 450\,\text{g})\).

Find the sum: \(4\,\text{kg}\,200\,\text{g} \div 60 + 12\,\text{kg} \div 80\).

A satellite needs exactly \(1\,\text{day}\ 5\,\text{h}\ 12\,\text{min}\) to complete a set of measurements. Find the total time in minutes.

A computer needs \(3000\,\text{min}\) to complete a large update. Write this time in days, hours, and minutes.

Evaluate each expression. a) \(2\,\text{h}-\frac{1}{4}\,\text{h}-55\,\text{min}\) b) \(3\times(12\,\text{min}\ 45\,\text{s})\) c) \(5\,\text{kg}\div 125\,\text{g}\) d) \(3\,\text{km}\ 50\,\text{m}-1\,\text{km}\ 200\,\text{m}\)

A delivery van carries packages that each weigh \(5\,\text{lb}\,8\,\text{oz}\). a) What is the total weight of \(18\) packages? b) The van can carry at most \(1320\,\text{lb}\) of cargo. What is the greatest number of these packages it can carry?

Evaluate both sides and write \(<\), \(>\), or \(=\). Show your calculations. a) \(10\,\text{h}\div 15\ \square\ 45\,\text{min}\) b) \(0.5\,\text{km}\times 8\ \square\ 3\,\text{km}\ 900\,\text{m}\) c) \(4\,\text{kg}-1\,\text{kg}\ 200\,\text{g}\ \square\ 14\times 200\,\text{g}\)

An elephant at a zoo is exactly \(2000\) days old. How many years and days is that? Use \(365\) days for one year.

A record says that an olive tree was planted \(1150\) months ago. A gardener claims, “The tree is already more than \(95\) years old.” Is the gardener correct? Justify your answer with a calculation.

Calculate: \(3\,\text{days}\ 18\,\text{h}\div15\)

Find the value of the quotient: \(4\,\text{h}\ 30\,\text{min}\div18\,\text{min}\)

Find the sum: \(1\,\text{day}\ 14\,\text{h}\ 45\,\text{min}+19\,\text{h}\ 30\,\text{min}\)

Evaluate each expression. Convert units when needed. a) \(3.4\,\text{kg}+850\,\text{g}-1.02\,\text{kg}+470\,\text{g}\) b) \(12\,\text{m}\ 5\,\text{cm}-4.8\,\text{m}+72\,\text{cm}\) c) \((4.2\,\text{kg}+580\,\text{g})\times 15\)

Evaluate each expression. Write time answers in hours and minutes. a) \(4\,\text{h}\ 12\,\text{min}-155\,\text{min}+1\,\text{h}\ 48\,\text{min}\) b) \(18\,\text{km}\div25\,\text{m}\) c) \(144\,\text{kg}\div12-3600\,\text{g}\div12\)

Evaluate each expression and write the result as a decimal in the larger unit. a) \(2\,\text{h}\ 30\,\text{min}+45\,\text{min}-1.25\,\text{h}\) b) \(6.3\,\text{kg}-(2100\,\text{g}+850\,\text{g})\)

Evaluate each expression and write the result as a decimal. a) \((15\,\text{m}\,60\,\text{cm} + 4.4\,\text{m}) \div 5\) b) \(0.85\,\text{km} - 320\,\text{m} + 1.2\,\text{km}\)

Evaluate each expression. Write each final answer as a decimal. a) \(2.5\,\text{h} + (1\,\text{h}\ 45\,\text{min} + 45\,\text{min})\) b) \(4.8\,\text{kg} \div 8 + 325\,\text{g} \times 4\)

A wooden fence has \(4\) sections, each \(6\,\text{ft}\) long. The fence will be made from vertical boards that are each \(6\,\text{in}\) wide, placed directly next to one another with no gaps. How many boards are needed altogether?

Find the missing measurement \(\square\) that makes the equation true: \(8\,\text{kg}\,450\,\text{g} - \square + 1250\,\text{g} = 7\,\text{kg}\,100\,\text{g}\).

Find the missing length: \(3.4\,\text{km} - 850\,\text{m} + \square = 4\,\text{km}\,20\,\text{m}\).

Complete the missing table entries and write each mass as a decimal in kilograms. <table> <tr> <th>\(100\,\text{kg}\)</th> <th>\(10\,\text{kg}\)</th> <th>\(1\,\text{kg}\)</th> <th>\(100\,\text{g}\)</th> <th>\(10\,\text{g}\)</th> <th>\(1\,\text{g}\)</th> <th>Decimal in kilograms</th> </tr> <tr><td>4</td><td>0</td><td>7</td><td>2</td><td>0</td><td>0</td><td>\(?\,\text{kg}\)</td></tr> <tr><td></td><td>5</td><td>0</td><td>3</td><td>0</td><td>0</td><td>\(?\,\text{kg}\)</td></tr> <tr><td>0</td><td>0</td><td>0</td><td>8</td><td>1</td><td>5</td><td>\(?\,\text{kg}\)</td></tr> <tr><td>1</td><td>2</td><td>0</td><td>4</td><td>5</td><td>0</td><td>\(?\,\text{kg}\)</td></tr> </table>

Enter each length in a place-value table with columns for kilometers, hundreds of meters, tens of meters, meters, tenths of a meter, hundredths of a meter, and thousandths of a meter. Then write each length as a decimal in meters. a) \(2\,\text{km}\ 45\,\text{m}\ 3\,\text{cm}\) b) \(80\,\text{m}\ 70\,\text{cm}\ 5\,\text{mm}\) c) \(6\,\text{km}\ 90\,\text{cm}\)

Three packages are weighed. Package A weighs \(1\,\text{kg}\ 25\,\text{g}\). Package B weighs \(1.205\,\text{kg}\). Package C weighs \(1250\,\text{g}\). a) Enter each mass in a place-value table with columns for \(1\,\text{kg}\), \(100\,\text{g}\), \(10\,\text{g}\), and \(1\,\text{g}\). b) Write all three masses as decimals in kilograms. c) Which package is heaviest?

Evaluate both sides. Then write \(<\), \(>\), or \(=\). a) \(1\,\text{km}-450\,\text{m}\ \square\ 500\,\text{m}+50\,\text{m}\) b) \(0.38\,\text{m}+22\,\text{cm}\ \square\ 0.6\,\text{m}-5\,\text{cm}\)

Santiago wrote: \(32\,\text{kg} \div 800\,\text{g} = 40\,\text{g}\). Find the error, explain it briefly, and give the correct result.

Check the calculation for an error and correct it: \(4\times15\,\text{min}+2\,\text{h}=62\,\text{min}\)

Sarah's goal is to read for exactly \(7\) hours this week. Her reading times from Monday through Saturday are shown below. <table> <tr><th>Day</th><th>Reading Time</th></tr> <tr><td>Monday</td><td>\(45\,\text{min}\)</td></tr> <tr><td>Tuesday</td><td>\(1\,\text{h}\ 10\,\text{min}\)</td></tr> <tr><td>Wednesday</td><td>\(55\,\text{min}\)</td></tr> <tr><td>Thursday</td><td>\(1\,\text{h}\ 20\,\text{min}\)</td></tr> <tr><td>Friday</td><td>\(40\,\text{min}\)</td></tr> <tr><td>Saturday</td><td>\(1\,\text{h}\ 5\,\text{min}\)</td></tr> </table> How long must Sarah read on Sunday to reach her goal?

An express train takes \(52\) minutes to travel from Riverton to Lakeview. A local train takes \(1\,\text{h}\ 14\,\text{min}\) for the same trip because it makes more stops. a) How many minutes faster is the express train on one trip? b) A commuter makes a round trip on \(5\) days each week. How much time would the commuter save in one week by switching from the local train to the express train? Give the answer in hours and minutes.

Evaluate the expression and write the result in meters and centimeters: \(15.6\,\text{m} \div 4 + 85\,\text{cm} \times 7\).

Evaluate and write the result using mixed units: \(2.5\,\text{kg} \times 9 - 14\,\text{kg}\,400\,\text{g} \div 6\).

Calculate and give the result in mixed time units: \(1\,\text{h}\ 45\,\text{min}+(3\,\text{h}\ 20\,\text{min})\div8\)

A coffee roaster packages coffee in \(1\)-pound bags and \(8\)-ounce bags. The roaster will package \(30\,\text{lb}\) of coffee and use the same number of each bag size. How many bags will be filled altogether?

Calculate. a) \(12\,\text{m}\,40\,\text{cm} - 85\,\text{cm}\) b) \(7 \times 3\,\text{m}\,20\,\text{cm}\) c) \(2\,\text{km} - 750\,\text{m}\) d) \(1\,\text{m} \div 5\,\text{mm}\)

Solve these time conversion and addition problems: a) How many hours and minutes are \(315\,\text{min}\)? b) Find \(1\,\text{h}\ 45\,\text{min}+230\,\text{min}\). Give the result in hours and minutes.

A leaky faucet loses exactly one drop every second. How many weeks, days, hours, minutes, and seconds will pass before \(10{,}000{,}000\) drops have fallen? Use \(1\) week \(= 7\) days.

Roadside marker posts will be placed along both sides of a straight highway from mile marker \(7\) to mile marker \(12\). On each side, the posts are spaced every \(200\,\text{ft}\), with posts at both endpoints. How many posts are needed altogether? Use \(1\,\text{mi} = 5280\,\text{ft}\).

Evaluate the expression and write the result as a decimal number of meters: \(5\,\text{m}\,4\,\text{cm} - 4 \times (15\,\text{cm} + 22\,\text{mm})\).

Two boards have a total length of \(4.50\,\text{m}\). One board is \(70\,\text{cm}\) shorter than the other. Find the length of each board in meters.

A cargo plane can carry at most \(25\) metric tons of payload. Use \(1\,\text{metric ton}=1000\,\text{kg}\). For a relief flight, workers load \(840\) crates with a mass of \(25\,\text{kg}\) each. Twelve support staff members also fly, with a combined person-and-equipment mass of \(120\,\text{kg}\) each. a) Find the current payload mass in kilograms. b) How many metric tons of payload capacity remain? c) By how many kilograms would the remaining capacity decrease if improved packaging added \(500\,\text{g}\) to every crate?

Find the missing duration \(\square\) that makes the equation true: \(1\,\text{h}\ 25\,\text{min}+140\,\text{s}+\square=2\,\text{h}\)

Two packages have a total mass of \(15.6\,\text{kg}\). The first package has a mass that is \(2\,\text{kg}\,400\,\text{g}\) greater than the second package. Find the mass of each package.