Decimal notation for tenths and hundredths

Learning goals

Connects tenths and hundredths fractions to decimal notation.
Reads and writes decimals to hundredths.
Uses place-value models to interpret decimal digits.
Converts between simple fractions with denominators 10 or 100 and decimals.

Difficulty: 1 – 5

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Decimal notation for tenths and hundredths 1

Which decimal is equivalent to $\frac{3}{5}$?

Hints

- Find an equivalent fraction with denominator $10$. - Recall how tenths are written as decimals.

Solution

1. Make an equivalent fraction with denominator $10$: $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$. 2. Write six tenths as a decimal: $\frac{6}{10} = 0.6$.

Answer

$0.6$

Decimal notation for tenths and hundredths 2

Write each decimal as a fraction with denominator $10$ or $100$. Do not simplify. a) $0.4$ b) $0.12$ c) $0.05$ d) $3.7$ e) $0.08$

Hints

- Count the decimal places to choose the denominator. - One decimal place means tenths; two decimal places mean hundredths. - Use all the digits as the numerator after removing the decimal point.

Solution

1. One decimal place represents tenths, and two decimal places represent hundredths. 2. For a), $0.4 = \frac{4}{10}$. 3. For b), $0.12 = \frac{12}{100}$. 4. For c), $0.05 = \frac{5}{100}$. 5. For d), $3.7 = \frac{37}{10}$. 6. For e), $0.08 = \frac{8}{100}$.

Answer

a) $\frac{4}{10}$ b) $\frac{12}{100}$ c) $\frac{5}{100}$ d) $\frac{37}{10}$ e) $\frac{8}{100}$

Decimal notation for tenths and hundredths 3

What portion of the circle is shaded? Write the answer as a fraction and as a decimal.

Hints

- Count the equal sectors around the circle. - Count the sectors that are shaded. - The first place after the decimal point means tenths.

Solution

1. The circle has $10$ equal sectors, and $1$ is shaded. 2. The shaded fraction is $\frac{1}{10}$. 3. One tenth is $0.1$ in decimal notation.

Answer

Fraction: $\frac{1}{10}$. Decimal: $0.1$.

Decimal notation for tenths and hundredths 4

What portion of the bar is shaded? Write your answer as a fraction and as a decimal.

Hints

- Count the equal sections of the bar. - Count just the shaded sections. - Write the fraction in tenths as a decimal.

Solution

1. Seven of the ten equal sections are shaded. 2. The shaded fraction is $\frac{7}{10}$. 3. Seven tenths is $0.7$.

Answer

Fraction: $\frac{7}{10}$. Decimal: $0.7$.

Decimal notation for tenths and hundredths 5

Write “four and seven tenths” as a decimal.

Hints

- Identify the whole-number part. - Place the $7$ in the tenths place.

Solution

1. The whole-number part is $4$. 2. Seven tenths is written as $0.7$. 3. The decimal is $4.7$.

Answer

$4.7$

Decimal notation for tenths and hundredths 6

Three number cards show $0.9$, $0.09$, and $9.0$. Which card shows nine tenths?

Hints

- Compare the place of the digit $9$ on each card. - The tenths place is immediately to the right of the decimal point.

Solution

1. Nine tenths means $9$ is in the tenths place. 2. The card showing $0.9$ has $9$ in the tenths place.

Answer

$0.9$

Decimal notation for tenths and hundredths 7

Write twelve and three hundredths as a decimal with exactly two digits after the decimal point.

Hints

- Identify the whole-number part. - Place the $3$ in the hundredths place and use a zero in the tenths place.

Solution

1. The whole-number part is $12$. 2. Three hundredths is written as $0.03$. 3. The decimal is $12.03$.

Answer

$12.03$

Decimal notation for tenths and hundredths 8

Read the decimal $5.2$ using place-value words.

Hints

- Identify the place of the digit to the right of the decimal point. - Use “and” to separate the whole-number part from the fractional part.

Solution

1. The whole-number part is $5$. 2. The digit $2$ is in the tenths place. 3. The decimal is read as “five and two tenths.”

Answer

“five and two tenths”

Decimal notation for tenths and hundredths 9

Complete the missing digit: $6.\square4$ represents six and twenty-four hundredths.

Hints

- Write twenty-four hundredths as two decimal digits. - Identify the tenths digit.

Solution

1. Twenty-four hundredths is written as $0.24$. 2. The tenths digit is $2$. 3. The completed decimal is $6.24$.

Answer

The missing digit is $2$; the decimal is $6.24$.

Decimal notation for tenths and hundredths 10

A price tag shows $\$3.05$. Read the amount in dollars and cents.

Hints

- The digits after the decimal point show cents. - Read $0.05$ as five hundredths of a dollar.

Solution

1. The whole-dollar amount is $3$. 2. The decimal part $0.05$ equals $5$ cents. 3. The amount is read as “three dollars and five cents.”

Answer

“three dollars and five cents”

Decimal notation for tenths and hundredths 11

A kitchen scale measures seventy-five hundredths of a pound. Write the mass as a decimal with its unit.

Hints

- Write seventy-five hundredths using two decimal places. - Include the unit in your answer.

Solution

1. Seventy-five hundredths is $\frac{75}{100}$. 2. As a decimal, $\frac{75}{100} = 0.75$. 3. The mass is $0.75\,\text{lb}$.

Answer

$0.75\,\text{lb}$

Decimal notation for tenths and hundredths 12

A thermometer shows $65.4\,\text{°F}$. Read the temperature using place-value words.

Hints

- Identify the place of the digit to the right of the decimal point. - Include the temperature unit in the reading.

Solution

1. The whole-number part is $65$. 2. The digit $4$ is in the tenths place. 3. The temperature is read as “sixty-five and four tenths degrees Fahrenheit.”

Answer

“sixty-five and four tenths degrees Fahrenheit”

Decimal notation for tenths and hundredths 13

An admission price is announced as twenty-four dollars and ninety cents. Write the price using decimal notation.

Hints

- Write the dollar amount before the decimal point. - Write cents using exactly two digits after the decimal point.

Solution

1. The whole-dollar amount is $24$. 2. Ninety cents is $\$0.90$. 3. The price is $\$24.90$.

Answer

$\$24.90$

Decimal notation for tenths and hundredths 14

The bar and the grid each represent one whole. How many small squares in the grid would you shade to show the same amount as the bar? Write an equivalent-fraction equation.

Hints

- Name the shaded fraction of the bar before looking at the grid. - How many small squares are in one column of the grid? - Think about how many columns match the shaded part of the bar.

Solution

1. The bar shows four tenths, or $\frac{4}{10}$, shaded. 2. The grid has ten columns, each with ten small squares. Matching four shaded tenths means shading four columns. 3. That is $4\times10=40$ squares, so $\frac{4}{10}=\frac{40}{100}$.

Answer

$40$ hundredths; $\frac{4}{10}=\frac{40}{100}$.

Decimal notation for tenths and hundredths 15

Complete the place-value chart for $0.07$. <table><tr><th>Ones</th><th>Tenths</th><th>Hundredths</th></tr><tr><td>$0$</td><td>$\square$</td><td>$\square$</td></tr></table>

Hints

- Count the places to the right of the decimal point. - The first place is tenths; the second is hundredths.

Solution

1. The first digit after the decimal point is the tenths digit, $0$. 2. The second digit is the hundredths digit, $7$.

Answer

Tenths: $0$; hundredths: $7$.

Decimal notation for tenths and hundredths 16

Write each decimal as a fraction in simplest form. a) $0.15$ b) $0.08$ c) $0.75$ d) $2.4$

Hints

- Use the number of decimal places to choose a denominator of $10$ or $100$. - Simplify by dividing the numerator and denominator by a common factor. - Check whether the numerator and denominator still share a factor.

Solution

1. For a), $0.15 = \frac{15}{100} = \frac{3}{20}$. 2. For b), $0.08 = \frac{8}{100} = \frac{2}{25}$. 3. For c), $0.75 = \frac{75}{100} = \frac{3}{4}$. 4. For d), $2.4 = \frac{24}{10} = \frac{12}{5}$.

Answer

a) $\frac{3}{20}$ b) $\frac{2}{25}$ c) $\frac{3}{4}$ d) $\frac{12}{5}$

Decimal notation for tenths and hundredths 17

Convert $\frac{11}{20}$ to a decimal.

Hints

- What number multiplies $20$ to make $100$? - Multiply the numerator by the same number. - You can check by dividing the numerator by the denominator.

Solution

1. Multiply the numerator and denominator by $5$: $\frac{11}{20} = \frac{55}{100}$. 2. Write the fraction with denominator $100$ as a decimal: $\frac{55}{100} = 0.55$. 3. The result can also be checked by division: $11 \div 20 = 0.55$.

Answer

$0.55$

Decimal notation for tenths and hundredths 18

Write $0.48$ as a fraction in simplest form.

Hints

- First write the decimal as a fraction with denominator $100$. - Find a common factor of the numerator and denominator. - Divide both by the same factor until the fraction is in simplest form.

Solution

1. Write the decimal as a fraction with denominator $100$: $0.48 = \frac{48}{100}$. 2. The greatest common factor of $48$ and $100$ is $4$. 3. Divide the numerator and denominator by $4$: $\frac{48 \div 4}{100 \div 4} = \frac{12}{25}$.

Answer

$\frac{12}{25}$

Decimal notation for tenths and hundredths 19

Find each missing number. a) $0.75 = \frac{75}{\square}$ b) $0.03 = \frac{\square}{100}$ c) $2.1 = \frac{\square}{10}$ d) $0.06 = \frac{6}{\square}$ e) $9 = \frac{\square}{100}$

Hints

- Use the place value of the last decimal digit. - A whole number can also be written as a fraction. - Think about how many hundredths equal one whole.

Solution

1. For a), $0.75$ is $75$ hundredths, so $\square = 100$. 2. For b), $0.03$ is $3$ hundredths, so $\square = 3$. 3. For c), $2.1$ is $21$ tenths, so $\square = 21$. 4. For d), $0.06$ is $6$ hundredths, so $\square = 100$. 5. For e), $9 = 9 \times \frac{100}{100} = \frac{900}{100}$, so $\square = 900$.

Answer

a) $100$ b) $3$ c) $21$ d) $100$ e) $900$

Decimal notation for tenths and hundredths 20

Write each money amount using a dollar sign and decimal notation. a) $9$ dollars $40$ cents b) $3$ dollars $8$ cents c) $0$ dollars $6$ cents d) $15$ dollars $55$ cents

Hints

- How many cents make one dollar? - Use two digits for the cents. - Add a zero placeholder when the cents amount has one digit.

Solution

1. Write dollars to the left of the decimal point and cents in the two places to the right. 2. Use a zero as a placeholder when the number of cents has only one digit. 3. The amounts are $\$9.40$, $\$3.08$, $\$0.06$, and $\$15.55$.

Answer

a) $\$9.40$ b) $\$3.08$ c) $\$0.06$ d) $\$15.55$

Decimal notation for tenths and hundredths 21

Write each missing money amount in words or decimal notation. a) $4$ dollars $7$ cents $=\ \square$ b) $\$0.12=\ \square$ c) $20$ dollars $80$ cents $=\ \square$ d) $\$1.01=\ \square$

Hints

- The two digits after the decimal point show the cents; use a zero placeholder when needed. - An amount less than one dollar has $0$ to the left of the decimal point.

Solution

1. Write $4$ dollars $7$ cents as $\$4.07$. 2. Write $\$0.12$ as $12$ cents. 3. Write $20$ dollars $80$ cents as $\$20.80$. 4. Write $\$1.01$ as $1$ dollar $1$ cent.

Answer

a) $\$4.07$ b) $12$ cents c) $\$20.80$ d) $1$ dollar $1$ cent

Decimal notation for tenths and hundredths 22

Which amounts are equal? Make three pairs from this list: $\$2.40$, $24$ cents, $2$ dollars $4$ cents, $\$0.24$, $2$ dollars $40$ cents, $\$2.04$.

Hints

- Rewrite all amounts in the same form. - Pay attention to whether the $4$ is in the tenths or hundredths place.

Solution

1. Express the amounts in matching forms. 2. $\$2.40$ equals $2$ dollars $40$ cents. 3. $\$0.24$ equals $24$ cents. 4. $\$2.04$ equals $2$ dollars $4$ cents.

Answer

$\$2.40$ and $2$ dollars $40$ cents $\$0.24$ and $24$ cents $\$2.04$ and $2$ dollars $4$ cents

Decimal notation for tenths and hundredths 23

Write each amount entirely in cents. a) $\$5.75$ b) $\$12.05$ c) $\$110.10$ d) $\$2.04$

Hints

- One dollar equals $100$ cents. - Think about what each digit after the decimal point represents in money. - Pay special attention to placeholder zeros in amounts such as $\$12.05$.

Solution

1. $\$5.75=575$ cents. 2. $\$12.05=1205$ cents. 3. $\$110.10=11{,}010$ cents. 4. $\$2.04=204$ cents.

Answer

a) $575$ cents b) $1205$ cents c) $11{,}010$ cents d) $204$ cents

Decimal notation for tenths and hundredths 24

In US currency, $\$1$ equals $100$ cents. a) Write $1$ cent, $5$ cents, and $40$ cents as decimal parts of $\$1$. b) Lucas says, “I have $\$0.25$ in my pocket.” Give two different ways he could have exactly this amount using pennies, nickels, dimes, and quarters.

Hints

- Think of one dollar as $100$ equal cents. - The hundredths place in a dollar amount records cents. - For part b), make two different coin totals that both equal $25$ cents.

Solution

1. One cent is one hundredth of a dollar, so it is $\$0.01$. 2. Five cents is five hundredths of a dollar, so it is $\$0.05$. 3. Forty cents is forty hundredths of a dollar, so it is $\$0.40$. 4. $\$0.25$ is $25$ cents. One possible coin combination is one quarter. 5. Another possible combination is two dimes and one nickel.

Answer

a) $\$0.01$, $\$0.05$, $\$0.40$ b) For example, one quarter; or two dimes and one nickel.

Decimal notation for tenths and hundredths 25

Write each number of cents in dollar notation. For example, $105$ cents is $\$1.05$. a) $804$ cents b) $2560$ cents c) $7003$ cents d) $15{,}020$ cents

Hints

- One dollar equals $100$ cents. - The last two digits show the number of cents. - Use a zero in the tenths place when the remaining number of cents has only one digit.

Solution

1. One dollar equals $100$ cents, so separate each amount into groups of $100$ cents and the remaining cents. 2. a) $804$ cents is $8$ dollars and $4$ cents, or $\$8.04$. 3. b) $2560$ cents is $25$ dollars and $60$ cents, or $\$25.60$. 4. c) $7003$ cents is $70$ dollars and $3$ cents, or $\$70.03$. 5. d) $15{,}020$ cents is $150$ dollars and $20$ cents, or $\$150.20$.

Answer

a) $\$8.04$ b) $\$25.60$ c) $\$70.03$ d) $\$150.20$

Decimal notation for tenths and hundredths 26

Complete the table for each money amount. <table> <thead><tr><th>Decimal dollars</th><th>Dollars and cents</th><th>Cents only</th></tr></thead> <tbody> <tr><td>$\$15.24$</td><td>$\square$</td><td>$\square$</td></tr> <tr><td>$\square$</td><td>$\$6$ and $2$ cents</td><td>$\square$</td></tr> <tr><td>$\square$</td><td>$\square$</td><td>$90$ cents</td></tr> <tr><td>$\$0.05$</td><td>$\square$</td><td>$\square$</td></tr> </tbody> </table>

Hints

- One dollar equals $100$ cents. - Dollar amounts use two decimal places for cents. - A placeholder zero is needed when the cents amount has only one digit.

Solution

1. $\$15.24$ is $\$15$ and $24$ cents, or $1524$ cents. 2. $\$6$ and $2$ cents is $\$6.02$, or $602$ cents. 3. $90$ cents is $\$0.90$, or $\$0$ and $90$ cents. 4. $\$0.05$ is $\$0$ and $5$ cents, or $5$ cents.

Answer

<table> <thead><tr><th>Decimal dollars</th><th>Dollars and cents</th><th>Cents only</th></tr></thead> <tbody> <tr><td>$\$15.24$</td><td>$\$15$ and $24$ cents</td><td>$1524$ cents</td></tr> <tr><td>$\$6.02$</td><td>$\$6$ and $2$ cents</td><td>$602$ cents</td></tr> <tr><td>$\$0.90$</td><td>$\$0$ and $90$ cents</td><td>$90$ cents</td></tr> <tr><td>$\$0.05$</td><td>$\$0$ and $5$ cents</td><td>$5$ cents</td></tr> </tbody> </table>

Decimal notation for tenths and hundredths 27

Fill in the blanks so each chain is correct. a) $\$24.08=\$\square$ and $\square$ cents $=\square$ cents b) $\$\square=\$3$ and $70$ cents $=\square$ cents c) $\$\square=\$\square$ and $\square$ cents $=1005$ cents d) $\$0.40=\$\square$ and $\square$ cents $=\square$ cents

Hints

- Cents occupy two decimal places in a dollar amount. - Think about how many cents make one whole dollar. - Use a placeholder zero when a cents amount has only one digit.

Solution

1. $\$24.08$ is $\$24$ and $8$ cents, or $2408$ cents. 2. $\$3$ and $70$ cents is $\$3.70$, or $370$ cents. 3. $1005$ cents is $\$10$ and $5$ cents, or $\$10.05$. 4. $\$0.40$ is $\$0$ and $40$ cents, or $40$ cents.

Answer

a) $\$24.08=\$24$ and $8$ cents $=2408$ cents b) $\$3.70=\$3$ and $70$ cents $=370$ cents c) $\$10.05=\$10$ and $5$ cents $=1005$ cents d) $\$0.40=\$0$ and $40$ cents $=40$ cents

Decimal notation for tenths and hundredths 28

What fraction of the figure is shaded? a) Write the shaded part as a fraction in simplest form. b) Write the shaded part as a decimal.

Hints

- Count the total number of equal squares and the shaded squares. - Simplify the shaded fraction before converting it. - To write the fraction as a decimal, look for an equivalent fraction with denominator $100$.

Solution

1. The grid has $5$ rows and $4$ columns, so it contains $5\times4=20$ equal squares. 2. There are $15$ shaded squares, so the fraction is $\frac{15}{20}$. 3. Simplify: $\frac{15}{20}=\frac{3}{4}$. 4. Rename fourths as hundredths: $\frac{3}{4}=\frac{75}{100}=0.75$.

Answer

a) $\frac{3}{4}$ b) $0.75$

Decimal notation for tenths and hundredths 29

The square is divided into $100$ equal smaller squares. What portion is shaded? Write the shaded portion as a fraction and as a decimal.

Hints

- How many small squares are in the whole grid? - Count the shaded squares. - A fraction with denominator $100$ can be written directly as a decimal.

Solution

1. One full row of $10$ squares and $2$ more squares are shaded, for a total of $10 + 2 = 12$ shaded squares. 2. Since $12$ of $100$ squares are shaded, the fraction is $\frac{12}{100}$. 3. Twelve hundredths is written as $0.12$.

Answer

Fraction: $\frac{12}{100}$ Decimal: $0.12$

Decimal notation for tenths and hundredths 30

Several full rows of the hundred grid are shaded. Write the shaded portion as a decimal and as a fraction in simplest form.

Hints

- Count the shaded squares out of $100$. - Write the portion as a decimal in hundredths. - Simplify the fraction by dividing the numerator and denominator by a common factor.

Solution

1. Eight full rows of $10$ squares are shaded, so $8 \times 10 = 80$ squares are shaded. 2. The shaded portion is $\frac{80}{100} = 0.80 = 0.8$. 3. Divide the numerator and denominator by $20$: $\frac{80}{100} = \frac{4}{5}$.

Answer

Decimal: $0.8$ Fraction in simplest form: $\frac{4}{5}$

Decimal notation for tenths and hundredths 31

What portion of the hundred grid is shaded? Write the answer as a fraction and as a decimal.

Hints

- Count the rows and columns in the shaded block. - Compare the shaded count with the total of $100$ squares. - Use the hundredths place when writing the decimal.

Solution

1. The shaded block is $3 \times 3$, so it contains $3 \times 3 = 9$ squares. 2. Since the grid has $100$ squares, the shaded fraction is $\frac{9}{100}$. 3. Nine hundredths is written as $0.09$.

Answer

Fraction: $\frac{9}{100}$ Decimal: $0.09$

Decimal notation for tenths and hundredths 32

A display requires exactly two digits after the decimal point. Enter two thousand and six tenths in the required format.

Hints

- First write the value using tenths. - Add a trailing zero so the display shows two decimal places.

Solution

1. Two thousand and six tenths is $2000.6$. 2. Adding a trailing zero does not change the value. 3. With exactly two digits after the decimal point, the entry is $2000.60$.

Answer

$2000.60$

Decimal notation for tenths and hundredths 33

Amara writes five hundred eight and nine hundredths as $508.9$. Check the entry and correct it.

Hints

- Identify the place named by “hundredths.” - Decide what must appear in the tenths place when there are no tenths. - Check the value of the decimal after placing the digits.

Solution

1. Nine hundredths means the $9$ belongs in the hundredths place. 2. A zero is needed in the tenths place. 3. The correct decimal is $508.09$.

Answer

Amara's entry is incorrect. The correct decimal is $508.09$.

Decimal notation for tenths and hundredths 34

Timo reads $0.04$ as “four tenths.” What place-value word did he use incorrectly? Give the correct reading.

Hints

- Locate the digit $4$ on a place-value chart. - Name the place that is two positions to the right of the decimal point.

Solution

1. The $4$ is two places to the right of the decimal point. 2. Therefore, the $4$ is in the hundredths place, not the tenths place. 3. The correct reading is “four hundredths.”

Answer

He used “tenths” incorrectly. The correct reading is “four hundredths.”

Decimal notation for tenths and hundredths 35

Which decimal represents five and two hundredths? A: $5.2$ B: $5.02$ C: $5.002$ D: $52.0$

Hints

- Identify the place named by “hundredths.” - Check whether the tenths place needs a zero placeholder.

Solution

1. The whole-number part is $5$. 2. The digit $2$ belongs in the hundredths place, so a zero is needed in the tenths place. 3. Choice B, $5.02$, is correct.

Answer

B: $5.02$

Decimal notation for tenths and hundredths 36

Complete the table. <table> <tr><th>Whole-number part</th><th>Hundredths</th><th>Decimal</th></tr> <tr><td>$0$</td><td>$48$</td><td>$\square$</td></tr> </table>

Hints

- Think about the fraction for forty-eight hundredths. - Use two places to the right of the decimal point.

Solution

1. The whole-number part is $0$. 2. Forty-eight hundredths places $4$ in the tenths place and $8$ in the hundredths place. 3. The decimal is $0.48$.

Answer

$0.48$

Decimal notation for tenths and hundredths 37

A number is two and thirty-five hundredths. Which two digits appear immediately after the decimal point, and what is the decimal?

Hints

- Write thirty-five hundredths using two decimal places. - Combine the fractional part with the whole-number part.

Solution

1. Thirty-five hundredths places $3$ in the tenths place and $5$ in the hundredths place. 2. The whole-number part is $2$. 3. The decimal is $2.35$.

Answer

The digits are $3$ and $5$; the decimal is $2.35$.

Decimal notation for tenths and hundredths 38

Complete the place-value statement for $7.05$: The decimal has $\square$ tenths and $\square$ hundredths.

Hints

- Look at the first and second digits to the right of the decimal point. - Match each digit to its place value.

Solution

1. The tenths digit is $0$. 2. The hundredths digit is $5$. 3. The decimal has $0$ tenths and $5$ hundredths.

Answer

$0$ tenths and $5$ hundredths

Decimal notation for tenths and hundredths 39

Lina writes twelve and three tenths as $12.03$. Find the error and write the correct decimal.

Hints

- Identify the place named by “tenths.” - Check the position of the digit $3$.

Solution

1. Three tenths means the digit $3$ belongs in the tenths place. 2. In $12.03$, the $3$ is in the hundredths place. 3. The correct decimal is $12.3$.

Answer

Lina placed the $3$ in the hundredths place. The correct decimal is $12.3$.

Decimal notation for tenths and hundredths 40

Zoe writes eight hundredths as $0.8$. Find the error and write the correct decimal.

Hints

- Identify the place named by “hundredths.” - Use a zero as a placeholder in the tenths place.

Solution

1. Eight hundredths places $8$ in the hundredths place. 2. A zero is needed in the tenths place. 3. The correct decimal is $0.08$.

Answer

Zoe placed the $8$ in the tenths place. The correct decimal is $0.08$.

Decimal notation for tenths and hundredths 41

Insert one decimal point into the digit string $4075$ so that the result is forty and seventy-five hundredths.

Hints

- Identify which digits form the whole-number part. - Keep the digits in their original order.

Solution

1. The whole-number part must be $40$. 2. The fractional part must be $75$ hundredths. 3. Place the decimal point after the second digit to get $40.75$.

Answer

$40.75$

Decimal notation for tenths and hundredths 42

Use the digits $3$ and $8$ in that order. Add exactly one zero and one decimal point to make three and eight hundredths.

Hints

- Keep the digits $3$ and $8$ in the given order. - Use the zero as a placeholder in the tenths place.

Solution

1. The whole-number part is $3$. 2. Eight hundredths requires $0$ in the tenths place and $8$ in the hundredths place. 3. The decimal is $3.08$.

Answer

$3.08$

Decimal notation for tenths and hundredths 43

Insert one decimal point into the digit string $1205$ so that the result is one hundred twenty and five tenths.

Hints

- Identify which digits form the whole-number part. - Keep the digits in their original order.

Solution

1. The whole-number part must be $120$. 2. The digit $5$ must be in the tenths place. 3. Place the decimal point before the $5$ to get $120.5$.

Answer

$120.5$

Decimal notation for tenths and hundredths 44

A display requires exactly two digits after the decimal point. Enter six and five tenths in the required format, then read the displayed value using place-value words.

Hints

- Write the value first using tenths. - Add a trailing zero without changing the value.

Solution

1. Six and five tenths is $6.5$. 2. Add a trailing zero to show exactly two decimal places: $6.50$. 3. The displayed value can be read as “six and fifty hundredths.”

Answer

$6.50$; “six and fifty hundredths”

Decimal notation for tenths and hundredths 45

Decompose $2.48$ into a whole number, a fraction in tenths, and a fraction in hundredths.

Hints

- Separate the digits by their place values. - The first digit after the decimal point counts tenths. - The second digit after the decimal point counts hundredths.

Solution

1. The whole-number part is $2$. 2. The digit $4$ represents $\frac{4}{10}$, and the digit $8$ represents $\frac{8}{100}$. 3. Therefore, $2.48=2+\frac{4}{10}+\frac{8}{100}$.

Answer

$2+\frac{4}{10}+\frac{8}{100}$

Decimal notation for tenths and hundredths 46

Write point A as a decimal and as a fraction in hundredths.

Hints

- Count small tick intervals from the origin using the labeled tenths as guides. - The marks between neighboring tenths are hundredths. - Write the same number of hundredths in both forms.

Solution

1. Every small tick is one hundredth. 2. A is at fourteen hundredths, so the decimal is $0.14$ and the fraction is $\frac{14}{100}$.

Answer

$0.14=\frac{14}{100}$

Decimal notation for tenths and hundredths 47

Write each model's shaded amount as a decimal. Explain how the two amounts differ, and say which is greater.

Hints

- Count shaded hundredths in both equal-size models. - Compare what the digit $4$ represents in each decimal. - Read decimal digits by place value, not by their order as whole digits.

Solution

1. Model a) has $40$ shaded hundredths, or $0.40=0.4$. 2. Model b) has $4$ shaded hundredths, or $0.04$. 3. Four tenths are ten times four hundredths, so model a) has ten times as much shading and $0.4>0.04$.

Answer

a) $0.40$ b) $0.04$ Model a) is greater and represents ten times as much as model b).

Decimal notation for tenths and hundredths 48

Lucas has $\$15.06$ in his savings jar. He says, “That is $156$ cents.” Is Lucas correct? Convert $\$15.06$ to cents and explain the mistake he probably made.

Hints

- How many cents equal one dollar? - First find how many cents are in $\$15$. - Then add the $6$ cents and compare your result with $156$.

Solution

1. One dollar equals $100$ cents. 2. Convert the whole dollars: $15 \times 100 = 1500$ cents. 3. Add the remaining $6$ cents: $1500 + 6 = 1506$ cents. 4. Since $1506 \ne 156$, Lucas is not correct. He likely treated $\$15$ as $150$ cents or left out a zero when writing the amount.

Answer

Lucas is not correct. $\$15.06$ equals $1506$ cents. He probably forgot that $\$15$ alone equals $1500$ cents.

Decimal notation for tenths and hundredths 49

Form three groups of three equivalent money amounts. $\$3.20$; $\$3$ and $2$ cents; $32$ cents; $\$3$ and $20$ cents; $\$3.02$; $320$ cents; $\$0.32$; $302$ cents; $\$0$ and $32$ cents

Hints

- Convert each amount to one common form before grouping. - Compare the resulting values carefully. - Pay attention to the difference between $2$ cents and $20$ cents.

Solution

1. $\$3.20=\$3$ and $20$ cents $=320$ cents. 2. $\$3.02=\$3$ and $2$ cents $=302$ cents. 3. $\$0.32=\$0$ and $32$ cents $=32$ cents.

Answer

Group 1: $\$3.20$, $\$3$ and $20$ cents, $320$ cents Group 2: $\$3.02$, $\$3$ and $2$ cents, $302$ cents Group 3: $\$0.32$, $\$0$ and $32$ cents, $32$ cents

Decimal notation for tenths and hundredths 50

Read the values of points $K$, $L$, and $M$ on the number line. Write each value as a decimal and as a fraction or mixed number in simplest form.

Hints

- Count the equal intervals from $0$ to $1$ to find the tick spacing. - Use the tick spacing to read each point. - Write each decimal as tenths and simplify.

Solution

1. There are $5$ equal intervals from $0$ to $1$, so each minor tick represents $1 \div 5 = 0.2$. 2. The points are $K = 0.4$, $L = 1.2$, and $M = 1.6$. 3. Convert $K$: $0.4 = \frac{4}{10} = \frac{2}{5}$. 4. Convert $L$: $1.2 = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}$. 5. Convert $M$: $1.6 = \frac{16}{10} = \frac{8}{5} = 1\frac{3}{5}$.

Answer

$K = 0.4 = \frac{2}{5}$ $L = 1.2 = 1\frac{1}{5}$ $M = 1.6 = 1\frac{3}{5}$

Decimal notation for tenths and hundredths 51

A decimal has a whole-number part of $3$. Its tenths digit is $3$ greater than its hundredths digit, and the two decimal digits have a sum of $9$. Find the decimal and write its fractional part as tenths plus hundredths.

Hints

- List digit pairs whose sum matches the clue. - Check which pair has the required difference and order. - Place the larger digit in the tenths position as stated.

Solution

1. The digit pair must have a sum of $9$ and differ by $3$. 2. The tenths digit is $6$ and the hundredths digit is $3$. 3. The decimal is $3.63$, and its fractional part is $\frac{6}{10}+\frac{3}{100}$.

Answer

$3.63=3+\frac{6}{10}+\frac{3}{100}$

Decimal notation for tenths and hundredths 52

The fraction $\frac{70}{100}$ is shown with four decimal cards: $0.7$, $0.70$, $0.07$, and $7.0$. Sort the cards into “equal to $\frac{70}{100}$” and “not equal,” and explain the role of each zero.

Hints

- Name the place value of the digit $7$ on each card. - A zero after the last nonzero decimal digit behaves differently from a zero before it. - Compare each card with seventy hundredths, not only with the digits shown.

Solution

1. $\frac{70}{100}=\frac{7}{10}$, so $0.7$ and $0.70$ are equal to the fraction. 2. In $0.70$, the final zero records zero additional hundredths and does not change the value. 3. In $0.07$, the zero holds the tenths place, so the value is seven hundredths. In $7.0$, the $7$ is in the ones place.

Answer

Equal: $0.7$, $0.70$. The final zero in $0.70$ adds no hundredths. Not equal: $0.07$, $7.0$. In $0.07$, the zero holds the tenths place; in $7.0$, the zero shows no tenths after seven ones.

Decimal notation for tenths and hundredths 53

Lena reads $4.06$ as “four and six tenths” and rewrites it as $4.6$. Explain the place-value error. Which number is greater, and by how many hundredths?

Hints

- Write both decimals as mixed numbers with hundredths. - Pay attention to the position of the digit $6$, not just its appearance. - Compare the fractional parts after giving them the same unit.

Solution

1. In $4.06$, the zero is in the tenths place and the $6$ is in the hundredths place, so the number is $4\frac{6}{100}$. 2. The number $4.6$ is $4\frac{60}{100}$. 3. Therefore, $4.6$ is greater by $\frac{60}{100}-\frac{6}{100}=\frac{54}{100}$.

Answer

The zero in $4.06$ is a necessary tenths placeholder. $4.6$ is greater by $54$ hundredths.

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Grade 4 math worksheets

Decimal notation for tenths and hundredths

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