Free Math Worksheets

- Identify the place value of the digit \(9\). - Identify the value of the first digit \(5\). - Match each nonzero digit to its expanded-form value.

1. The digit \(5\) in \(509{,}014\) has a value of \(500{,}000\). 2. The digit \(9\) has a value of \(9000\), the digit \(1\) has a value of \(10\), and the digit \(4\) has a value of \(4\). 3. Therefore, \(509{,}014 = 500{,}000 + 9000 + 10 + 4\), which is choice d).

d) \(500{,}000 + 9000 + 10 + 4\)

- Say the number name in two parts, separated at “thousand.” - Decide which places in the final three digits need zeros.

1. The thousands period is two hundred forty-six, or \(246\). 2. The ones period is eighteen, which must be written as \(018\) after the thousands period. 3. The catalog number is \(246{,}018\).

\(246{,}018\)

- Read the digits before the comma first, then say “thousand.” - Read the final three digits as a number, using spaces and hyphens according to standard English conventions.

1. Read \(518\) in the thousands period as five hundred eighteen thousand. 2. Read \(407\) in the ones period as four hundred seven. 3. The complete number name is five hundred eighteen thousand four hundred seven.

five hundred eighteen thousand four hundred seven

- Separate the number name at the word “thousand.” - Decide which place in the final three digits needs a zero.

1. The thousands period is eight hundred eight, or \(808\). 2. The ones period is sixty-two, or \(62\), so write \(062\) in the final three places. 3. The number in standard form is \(808{,}062\).

\(808{,}062\)

- Do not say “zero” for empty place values in a whole-number name. - Read the thousands period first and then the remaining part.

1. The thousands period is \(700\), which is read as seven hundred thousand. 2. The final three digits are \(005\), which are read as five. 3. The complete number name is seven hundred thousand five.

seven hundred thousand five

- Separate the number name at “thousand.” - Check which places in the numeral must contain zeros.

1. Nine hundred nine thousand is \(909{,}000\). 2. Ninety is \(90\), so zeros are needed in the hundreds and ones places of the final period. 3. The number is \(909{,}090\).

\(909{,}090\)

- Focus only on the digits after the comma. - Decide what number those three digits name when leading zeros are not spoken.

1. The digits after the comma are \(004\), which represent \(4\). 2. The missing word is four. 3. The complete number name is five hundred seventy-three thousand four.

five hundred seventy-three thousand four

- Identify the place value of the \(1\). - The number name uses two words.

1. The digit \(1\) is in the millions place. 2. The number \(1{,}000{,}000\) is read as one million.

one million

- Separate the number name at “thousand.” - Add the needed zero in the final three-digit period.

1. The thousands period is nine hundred eleven, or \(911\). 2. The final part is eleven, which is written as \(011\) in the ones period. 3. The complete number is \(911{,}011\).

\(911{,}011\)

- Read the number in its two periods. - Combine the parts using standard spaces and hyphens.

1. The thousands period \(458\) is read as four hundred fifty-eight thousand. 2. The final period \(246\) is read as two hundred forty-six. 3. The complete number name is four hundred fifty-eight thousand two hundred forty-six.

four hundred fifty-eight thousand two hundred forty-six

- Separate the thousands period from the final three digits. - Use standard spaces and hyphens in the number name.

1. The thousands period \(845\) is read as eight hundred forty-five thousand. 2. The final period \(084\) is read as eighty-four. 3. The complete number name is eight hundred forty-five thousand eighty-four.

eight hundred forty-five thousand eighty-four

- Read the thousands period first. - Zeros used as placeholders are not spoken as separate words.

1. The thousands period \(608\) is read as six hundred eight thousand. 2. The final period \(006\) is read as six. 3. The word form is six hundred eight thousand six.

six hundred eight thousand six

- Separate the number name at “thousand.” - Use zeros in the places that are not named.

1. The thousands period is eight hundred ninety, or \(890\). 2. The final part is ninety, which is written as \(090\) in the ones period. 3. The complete number is \(890{,}090\).

\(890{,}090\)

- Separate the number into its thousands period and final three digits. - Combine the spoken parts using standard spaces and hyphens.

1. The thousands period \(342\) is read as three hundred forty-two thousand. 2. The final period \(708\) is read as seven hundred eight. 3. The complete number name is three hundred forty-two thousand seven hundred eight.

three hundred forty-two thousand seven hundred eight

- Listen for the word “thousand.” - The words before “thousand” describe the thousands period. - A place that is not named may need a zero as a placeholder. - Use commas to separate the periods in each number.

1. Separate each number name into its thousands period and ones period. 2. For a), eight hundred twelve thousand is \(812{,}000\), and four hundred fifty is \(450\). Together, the number is \(812{,}450\). 3. For b), six hundred thousand is \(600{,}000\), and seven hundred three is \(703\). Together, the number is \(600{,}703\). 4. For c), twenty-nine thousand is \(29{,}000\), and eighteen is \(18\). Together, the number is \(29{,}018\). 5. For d), seven hundred five thousand is \(705{,}000\), and five hundred five is \(505\). Together, the number is \(705{,}505\).

a) \(812{,}450\) b) \(600{,}703\) c) \(29{,}018\) d) \(705{,}505\)

- Use the comma to separate the number into periods. - Read the digits to the left of the comma, then say “thousand.” - Read the final three digits as a number, leaving out places whose digits are zero. - In standard US number names for whole numbers, do not use “and.”

1. Read each number by periods, beginning with the thousands period. 2. For a), \(320\) in the thousands period is “three hundred twenty thousand,” and \(45\) in the ones period is “forty-five.” The number name is three hundred twenty thousand forty-five. 3. For b), \(508\) in the thousands period is “five hundred eight thousand,” and \(900\) is “nine hundred.” The number name is five hundred eight thousand nine hundred. 4. For c), \(17\) in the thousands period is “seventeen thousand,” and \(206\) is “two hundred six.” The number name is seventeen thousand two hundred six. 5. For d), \(999\) in the thousands period is “nine hundred ninety-nine thousand,” and the ones period is zero. The number name is nine hundred ninety-nine thousand.

a) three hundred twenty thousand forty-five b) five hundred eight thousand nine hundred c) seventeen thousand two hundred six d) nine hundred ninety-nine thousand

- A place-value chart can help you put each digit in the correct position. - Write a zero in any place value that is missing. - In part c), notice that the greatest named place is the ten-thousands place.

1. For a), place the digits \(4\), \(2\), \(5\), \(8\), \(3\), and \(1\) in order from the hundred-thousands place to the ones place. The number is \(425{,}831\), or four hundred twenty-five thousand eight hundred thirty-one. 2. For b), retain the given zeros as placeholders. The number is \(700{,}409\), or seven hundred thousand four hundred nine. 3. For c), the unlisted hundred-thousands, hundreds, and ones places contain zeros. The number is \(16{,}050\), or sixteen thousand fifty.

a) \(425{,}831\); four hundred twenty-five thousand eight hundred thirty-one b) \(700{,}409\); seven hundred thousand four hundred nine c) \(16{,}050\); sixteen thousand fifty

- Identify the value of each nonzero digit. - Write one addend for each nonzero place. - A zero digit does not need its own addend.

1. a) \(49=40+9\). 2. b) \(166=100+60+6\). 3. c) \(944=900+40+4\). 4. d) \(2024=2000+20+4\). The zero in the hundreds place means there is no hundreds term.

a) \(40+9\) b) \(100+60+6\) c) \(900+40+4\) d) \(2000+20+4\)

- Match each addend with its place value. - Combine the thousands, hundreds, tens, and ones. - Check that every addend appears in the standard number.

1. a) \(70+4=74\). 2. b) \(400+40+4=444\). 3. c) \(900+90+9=999\). 4. d) \(1000+800+80+8=1888\).

a) \(74\) b) \(444\) c) \(999\) d) \(1888\)

- Try placing the digits in a place-value chart. - Listen for the words “hundred” and “thousand” and notice which place values are not named. - Read your completed numeral aloud to check that it matches the number name.

1. For a), one hundred thousand eight hundred has \(1\) in the hundred-thousands place and \(8\) in the hundreds place: \(100{,}800\). 2. For b), five hundred thousand twenty-two has \(5\) in the hundred-thousands place, \(2\) in the tens place, and \(2\) in the ones place: \(500{,}022\). 3. For c), thirty-seven thousand four has \(3\) in the ten-thousands place, \(7\) in the thousands place, and \(4\) in the ones place: \(37{,}004\). 4. For d), nine hundred nine thousand ninety has \(9\) in the hundred-thousands place, \(9\) in the thousands place, and \(9\) in the tens place: \(909{,}090\). 5. For e), twelve thousand seven hundred three has \(1\) in the ten-thousands place, \(2\) in the thousands place, \(7\) in the hundreds place, and \(3\) in the ones place: \(12{,}703\).

a) \(100{,}800\) b) \(500{,}022\) c) \(37{,}004\) d) \(909{,}090\) e) \(12{,}703\)

- Place each digit in the position named. - The zero is an important placeholder even though it is not spoken in the number name. - Read the number by periods.

1. Reading the place-value digits from left to right gives \(5\), \(2\), \(0\), \(8\), \(4\), and \(1\). 2. The number in standard form is \(520{,}841\). 3. The thousands period \(520\) is five hundred twenty thousand, and the final period \(841\) is eight hundred forty-one. 4. The complete word form is five hundred twenty thousand eight hundred forty-one.

Standard form: \(520{,}841\) Word form: five hundred twenty thousand eight hundred forty-one

- Find the total value represented in each column. - Six chips in the ten-thousands column represent \(60{,}000\). - You may omit a place-value term whose value is \(0\).

1. The chart shows \(6\) chips in the ten-thousands column, \(2\) in the thousands column, \(8\) in the hundreds column, \(0\) in the tens column, and \(4\) in the ones column. 2. Their values are \(60{,}000\), \(2000\), \(800\), \(0\), and \(4\). 3. Omitting the zero term, the expanded form is \(60{,}000 + 2000 + 800 + 4\).

\(60{,}000 + 2000 + 800 + 4\)

- Focus on the final part of the number name. - Read both numerals aloud and compare them with what the app heard.

1. Seven hundred thirty thousand is \(730{,}000\). 2. Six hundred fourteen is \(614\), not \(640\). 3. The correct entry is \(730{,}614\).

\(730{,}614\)

- Use the bounds to identify the thousands period. - Then place the tile naming the amount less than \(100\) after “thousand.”

1. The bounds show that the number has \(405\) in the thousands period and a value from \(1\) through \(99\) in the ones period. 2. Place “four hundred five” before “thousand” and “twenty-six” after it. 3. The complete number name is four hundred five thousand twenty-six. 4. In standard form, the number is \(405{,}026\).

four hundred five thousand twenty-six; \(405{,}026\)

- Read the digits in the thousands period first. - Then read the final three digits and compare each choice carefully.

1. The thousands period is \(391\), which is read as three hundred ninety-one thousand. 2. The ones period is \(204\), which is read as two hundred four. 3. Therefore, the correct word form is three hundred ninety-one thousand two hundred four.

a) three hundred ninety-one thousand two hundred four

- Read each number name all the way to the end. - Pay attention to the positions of the zeros in each numeral.

1. \(304{,}040\) has \(304\) in the thousands period and \(40\) in the ones period, so A matches three hundred four thousand forty. 2. \(340{,}004\) has \(340\) in the thousands period and \(4\) in the ones period, so B matches three hundred forty thousand four. 3. \(430{,}400\) has \(430\) in the thousands period and \(400\) in the ones period, so C matches four hundred thirty thousand four hundred.

A: three hundred four thousand forty B: three hundred forty thousand four C: four hundred thirty thousand four hundred

- Read the numeral by periods. - Pay attention to the zero in the hundreds place of the final period.

1. The thousands period, \(245\), is read as two hundred forty-five thousand. 2. The final three digits are \(036\), which are read as thirty-six, not three hundred six. 3. The correct number name is two hundred forty-five thousand thirty-six.

two hundred forty-five thousand thirty-six

- Read the numeral by periods. - Determine the place value of the \(8\) in the final three digits.

1. The thousands period, \(680\), is read as six hundred eighty thousand. 2. The final three digits are \(080\), which are read as eighty, not eight hundred. 3. The correct number name is six hundred eighty thousand eighty.

six hundred eighty thousand eighty

- Read the numeral by periods. - Compare the digits in the thousands period with the incorrect number name.

1. The thousands period is \(909\), which is read as nine hundred nine thousand. 2. The final three digits are \(099\), which are read as ninety-nine. 3. The correct number name is nine hundred nine thousand ninety-nine.

nine hundred nine thousand ninety-nine

- Work with one drawer number at a time. - Read each number by periods and omit place values whose digits are zero.

1. For a), \(504{,}050\) has \(504\) in the thousands period and \(50\) in the ones period, so it is five hundred four thousand fifty. 2. For b), \(540{,}005\) has \(540\) in the thousands period and \(5\) in the ones period, so it is five hundred forty thousand five. 3. For c), \(450{,}500\) has \(450\) in the thousands period and \(500\) in the ones period, so it is four hundred fifty thousand five hundred.

a) five hundred four thousand fifty b) five hundred forty thousand five c) four hundred fifty thousand five hundred

- Read each choice as a complete number. - Compare the thousands period first and then the final three digits.

1. Eight hundred eighty-one thousand gives \(881\) in the thousands period. 2. Eighteen gives \(018\) in the ones period. 3. The called number is \(881{,}018\), which is the second choice.

\(881{,}018\)

- Compare the digits of \(499{,}000\) and \(409{,}000\) from left to right. - Identify the place value that differs.

1. Four hundred ninety-nine thousand represents \(499{,}000\), which has \(9\) in the ten-thousands place. 2. The number \(409{,}000\) has \(0\) in the ten-thousands place and \(9\) in the thousands place. 3. The correct number name is four hundred nine thousand.

The incorrect label places a \(9\) in the ten-thousands place. The correct number name is four hundred nine thousand.

- Leave the correct part before “thousand” unchanged. - Compare only the words after “thousand” with the final three digits.

1. The thousands part, eight hundred twenty-one thousand, correctly represents \(821{,}000\). 2. The final three digits are \(012\), which are read as twelve, not one hundred twenty. 3. The correct number name is eight hundred twenty-one thousand twelve.

eight hundred twenty-one thousand twelve

- Read the numeral by periods. - Compare the tens and ones digits with the incorrect label.

1. The thousands period, \(654\), is read as six hundred fifty-four thousand. 2. The final three digits are \(321\), which are read as three hundred twenty-one, not three hundred twelve. 3. The correct number name is six hundred fifty-four thousand three hundred twenty-one.

six hundred fifty-four thousand three hundred twenty-one

- Separate the number name at “thousand.” - Check whether the two number parts were put in the correct periods.

1. The thousands period is two hundred fourteen, or \(214\). 2. The final part is forty, which is written as \(040\) in the ones period. 3. The correct number is \(214{,}040\).

\(214{,}040\)

- Work with each dictated number separately. - Use zeros as placeholders in every place value that is not named.

1. For a), one hundred nine thousand nine is \(109{,}009\). 2. For b), three hundred ninety thousand ninety is \(390{,}090\). 3. For c), nine hundred three thousand three is \(903{,}003\).

a) \(109{,}009\) b) \(390{,}090\) c) \(903{,}003\)

- Identify the part of each number name before “thousand.” - Then write the remaining part in the final three places, using zeros as needed.

1. For a), four hundred eleven thousand four is \(411{,}004\). 2. For b), seven hundred forty thousand eighty is \(740{,}080\). 3. For c), eight hundred eight thousand eight hundred is \(808{,}800\).

a) \(411{,}004\) b) \(740{,}080\) c) \(808{,}800\)

- Compare the digits place by place. - Remember that zeros used as placeholders are not spoken in a whole-number name.

1. For a), \(600{,}006\) has \(600\) in the thousands period and \(6\) in the ones period, so it is six hundred thousand six. 2. For b), \(606{,}060\) has \(606\) in the thousands period and \(60\) in the ones period, so it is six hundred six thousand sixty. 3. For c), \(660{,}600\) has \(660\) in the thousands period and \(600\) in the ones period, so it is six hundred sixty thousand six hundred.

a) six hundred thousand six b) six hundred six thousand sixty c) six hundred sixty thousand six hundred

- Read the thousands period first and then the final three digits. - Compare your word form with the pirate’s reading.

1. The thousands period \(707\) is read as seven hundred seven thousand. 2. The final period \(007\) is read as seven. 3. The complete number name is seven hundred seven thousand seven, so the pirate is correct.

Yes. The correct word form is seven hundred seven thousand seven.

- Group the digits into one whole number instead of naming each digit. - Do not say the placeholder zeros separately.

1. The digits form the number \(410{,}020\). 2. The thousands period \(410\) is read as four hundred ten thousand. 3. The final period \(020\) is read as twenty. 4. The whole number is read as four hundred ten thousand twenty.

four hundred ten thousand twenty

- Distinguish between the value of the whole number and a sequence of individual digits. - In the second reading, name every digit, including each zero.

1. As a whole number, \(507{,}042\) is read as five hundred seven thousand forty-two. 2. Digit by digit, it is read as five, zero, seven, zero, four, two.

Whole number: five hundred seven thousand forty-two. Digit by digit: five, zero, seven, zero, four, two.

- Read the number by periods. - Count place values from the right to locate the tens place.

1. The thousands period \(275\) is read as two hundred seventy-five thousand. 2. The final period \(418\) is read as four hundred eighteen. 3. The complete number name is two hundred seventy-five thousand four hundred eighteen. 4. In \(275{,}418\), the digit in the tens place is \(1\).

The number name is two hundred seventy-five thousand four hundred eighteen. The digit in the tens place is \(1\).

- Compare the thousands period in each choice first. - Then check the final three digits.

1. The thousands period of \(716{,}016\) is \(716\), read as seven hundred sixteen thousand. 2. The final period is \(016\), read as sixteen. 3. Therefore, choice a) is correct.

a) seven hundred sixteen thousand sixteen

- Identify the number spoken before “thousand.” - Then compare the final part with the last three digits of each choice.

1. The part before “thousand” is five hundred six, so the thousands period is \(506\). 2. The final part is sixty, so the ones period is \(060\). 3. The display should show \(506{,}060\).

\(506{,}060\)

- Treat each label as a whole number rather than a string of digits. - Pay close attention to zeros in the thousands and ones periods.

1. For a), \(101{,}010\) has \(101\) in the thousands period and \(10\) in the ones period, so it is one hundred one thousand ten. 2. For b), \(110{,}001\) has \(110\) in the thousands period and \(1\) in the ones period, so it is one hundred ten thousand one. 3. For c), \(111{,}100\) has \(111\) in the thousands period and \(100\) in the ones period, so it is one hundred eleven thousand one hundred.

a) one hundred one thousand ten b) one hundred ten thousand one c) one hundred eleven thousand one hundred

- Keep the two dictated numbers separate. - Check the thousands period and final two-digit number in each one.

1. For a), six hundred eighty-three thousand thirty-eight is \(683{,}038\). 2. For b), six hundred thirty-eight thousand eighty-three is \(638{,}083\).

a) \(683{,}038\) b) \(638{,}083\)

- Work with the numbers one at a time. - Read each number by periods and check the final two-digit part carefully.

1. For a), \(616{,}016\) is six hundred sixteen thousand sixteen. 2. For b), \(660{,}061\) is six hundred sixty thousand sixty-one.

a) six hundred sixteen thousand sixteen b) six hundred sixty thousand sixty-one

- Read the thousands period first. - Then compare the final three digits with each choice.

1. The thousands period of \(400{,}008\) is \(400\), which is read as four hundred thousand. 2. The final period is \(008\), which is read as eight. 3. Therefore, choice b) is correct.

b) four hundred thousand eight

- Treat all six digits as one whole number. - Read the three digits after the comma as a complete number.

1. The thousands period \(199\) is read as one hundred ninety-nine thousand. 2. The final period \(901\) is read as nine hundred one. 3. The full number name is one hundred ninety-nine thousand nine hundred one.

one hundred ninety-nine thousand nine hundred one

- Separate the number name at “thousand.” - Check the hundreds and tens places in the final period.

1. The thousands period is four hundred forty-four, or \(444\). 2. The final part is forty-four, which is written as \(044\) in the ones period. 3. The correct numeral is \(444{,}044\).

\(444{,}044\)

- Compare the beginning of the number name with the digit in the hundred-thousands place. - Add only the missing place-value word.

1. The thousands period is \(732\), which is read as seven hundred thirty-two. 2. The missing word after seven is hundred. 3. The complete number name is seven hundred thirty-two thousand thirty-two.

seven hundred thirty-two thousand thirty-two

- Read each choice slowly and identify its thousands period. - Convert both word forms to standard form before choosing.

1. One hundred five thousand five represents \(105{,}005\). 2. One hundred fifty thousand five represents \(150{,}005\). 3. Therefore, the first word form is correct for \(105{,}005\).

The correct form is one hundred five thousand five. It represents \(105{,}005\); the other form represents \(150{,}005\).

- Decide whether a final zero period is spoken in a whole-number name. - Read the numeral as one complete number.

1. The final three digits are all zeros. 2. A zero period at the end of a whole number is not spoken. 3. The correct number name is seven hundred thousand.

seven hundred thousand

- Remove only the zeros at the very beginning. - Then read the remaining digits as one whole number.

1. Leading zeros do not change the value of a whole number. 2. Removing only the leading zeros gives \(3070\). 3. The word form is three thousand seventy.

\(3070\); three thousand seventy

- Convert each spoken number to standard form independently. - Match the filenames only after both conversions are complete.

1. Track A, eight hundred eighteen thousand eighty, represents \(818{,}080\). 2. Track B, eight hundred eighty thousand eighteen, represents \(880{,}018\). 3. Therefore, Track A matches \(818{,}080\), and Track B matches \(880{,}018\).

Track A: \(818{,}080\) Track B: \(880{,}018\)

- Compare the thousands period of the two labels first. - Then check the final three digits.

1. The thousands period of \(919{,}019\) is \(919\), read as nine hundred nineteen thousand. 2. The final period is \(019\), read as nineteen. 3. The matching label is nine hundred nineteen thousand nineteen.

nine hundred nineteen thousand nineteen

- Compare the thousands period in each choice. - Then check the value represented by the final three digits.

1. The thousands period \(642\) is read as six hundred forty-two thousand. 2. The final period \(042\) is read as forty-two. 3. Therefore, choice b) is correct.

b) six hundred forty-two thousand forty-two

- Separate the number name at “thousand.” - Convert the part after “thousand” once as part of the full numeral and once by itself.

1. The full number name represents \(476{,}076\). 2. The part after “thousand” is seventy-six. 3. As a separate number, that final part is \(76\).

\(476{,}076\); final part: \(76\)

- Read the complete number first. - Then focus only on the final three digits.

1. The thousands period \(674\) is read as six hundred seventy-four thousand. 2. The final period \(604\) is read as six hundred four. 3. The complete number name is six hundred seventy-four thousand six hundred four. 4. The final part by itself is six hundred four.

six hundred seventy-four thousand six hundred four; final part: six hundred four

- Identify which quantities are still written as numerals. - Change only the number representations, not the rest of the sentence.

1. \(312{,}012\) is three hundred twelve thousand twelve. 2. Five hundred four thousand fifty is already in word form and remains unchanged. 3. \(90{,}009\) is ninety thousand nine. 4. The revised sentence is: “The first archive section has three hundred twelve thousand twelve image files, the second has five hundred four thousand fifty, and the third has ninety thousand nine.”

“The first archive section has three hundred twelve thousand twelve image files, the second has five hundred four thousand fifty, and the third has ninety thousand nine.”

- Identify which numbers are in word form and which one is already in standard form. - Keep the original order and sentence structure.

1. Two hundred eleven thousand eleven is \(211{,}011\). 2. \(502{,}020\) is already in standard form and remains unchanged. 3. Seven hundred fifty thousand five is \(750{,}005\). 4. The revised sentence is: “The groups have the numbers \(211{,}011\), \(502{,}020\), and \(750{,}005\).”

“The groups have the numbers \(211{,}011\), \(502{,}020\), and \(750{,}005\).”

- Separate the number name at “thousand.” - Compare the positions of the zeros in the answer choices.

1. The thousands period is five hundred seven, or \(507\). 2. The final part is five, which is written as \(005\) in the ones period. 3. The number is \(507{,}005\), so choice c) is correct.

c) \(507{,}005\)

- Use the pauses to identify the number periods. - Write the final number name with standard English spacing.

1. The pauses separate the spoken periods but do not change the number. 2. Six hundred four thousand seventeen is \(604{,}017\). 3. The standard word form is six hundred four thousand seventeen.

\(604{,}017\); six hundred four thousand seventeen

- Read the numeral as a whole number, not as a sequence of digits. - Check whether any choice unnecessarily says “zero.”

1. Zeros used as placeholders are not spoken separately when a numeral is read as a whole number. 2. The thousands period is \(305\), and the final nonzero digit is \(7\). 3. Therefore, \(305{,}007\) is three hundred five thousand seven, so choice a) is correct.

a) three hundred five thousand seven

- Compare the spoken thousands period with the digits before the comma. - Then reread the entire number.

1. Two thousand four represents \(2004\). 2. The index instead shows \(20{,}004\), which has \(20\) in the thousands period. 3. The correct reading is twenty thousand four.

twenty thousand four

- Work with each number separately and identify its thousands period. - Check carefully which zeros are placeholders and are not spoken.

1. For a), \(100{,}001\) is one hundred thousand one. 2. For b), \(101{,}010\) is one hundred one thousand ten. 3. For c), \(110{,}100\) is one hundred ten thousand one hundred. 4. For d), \(111{,}000\) is one hundred eleven thousand. 5. For e), \(10{,}111\) is ten thousand one hundred eleven. 6. For f), \(1101\) is one thousand one hundred one.

a) one hundred thousand one b) one hundred one thousand ten c) one hundred ten thousand one hundred d) one hundred eleven thousand e) ten thousand one hundred eleven f) one thousand one hundred one

- Group the digits from right to left in sets of three. - Then read the grouped number as a whole number.

1. Starting from the right, separate the digits into groups of three. 2. The grouped numeral is \(735{,}090\). 3. The word form is seven hundred thirty-five thousand ninety.

\(735{,}090\); seven hundred thirty-five thousand ninety

- For part b, write only the nonzero place-value parts. - In part c, remember that \(10\) hundreds can be regrouped as \(1\) thousand. - Add the place-value amounts to check each standard-form number.

1. For a), \(60{,}000 + 400 + 30 + 8 = 60{,}438\). 2. For b), the nonzero place values are \(300{,}000\), \(5000\), and \(70\), so \(305{,}070 = 300{,}000 + 5000 + 70\). 3. For c), \(12\) thousands is \(12{,}000\), \(15\) hundreds is \(1500\), and \(3\) ones is \(3\). Their sum is \(12{,}000 + 1500 + 3 = 13{,}503\).

a) \(60{,}438\) b) \(300{,}000 + 5000 + 70\) c) \(13{,}503\)

- Write the value represented by each column. - Only the tens term changes when two chips are removed from the tens column.

1. The chart shows \(8\) chips in the ten-thousands column, \(1\) in the thousands column, \(4\) in the hundreds column, \(5\) in the tens column, and \(6\) in the ones column. 2. Its expanded form is \(80{,}000 + 1000 + 400 + 50 + 6 = 81{,}456\). 3. Removing two tens chips changes \(5\) tens to \(3\) tens, so the tens term becomes \(30\). 4. The new expanded form is \(80{,}000 + 1000 + 400 + 30 + 6 = 81{,}436\).

Original: \(80{,}000 + 1000 + 400 + 50 + 6 = 81{,}456\) New: \(80{,}000 + 1000 + 400 + 30 + 6 = 81{,}436\)

- Convert the numeral and the label separately. - Compare the thousands period and the ones period in both representations.

1. Three hundred seventy-six thousand sixty-seven is \(376{,}067\). 2. This does not match \(367{,}076\). 3. The thousands period \(367\) is three hundred sixty-seven, and the final period \(076\) is seventy-six. 4. The correct label is three hundred sixty-seven thousand seventy-six.

No. The correct word form is three hundred sixty-seven thousand seventy-six.

- Write the thousands period and the final part separately. - Combine the two periods only after checking each one.

1. The thousands period in the announcement is nine hundred sixty-three, or \(963\). 2. The final part is thirty-six, which is written as \(036\) in the ones period. 3. The helper reversed the digits \(3\) and \(6\) in both periods. The correct number is \(963{,}036\).

The digits \(3\) and \(6\) were transposed in both periods. The correct number is \(963{,}036\).

- Convert Noah’s number name to standard form before comparing it with the given numeral. - Check the thousands period and the final three digits separately.

1. One hundred eighty thousand eight represents \(180{,}008\), not \(108{,}080\). 2. The number \(108{,}080\) is read as one hundred eight thousand eighty. 3. Noah changed both the thousands period and the final three digits when he wrote the number name.

\(108{,}080\) — one hundred eight thousand eighty; \(180{,}008\) — one hundred eighty thousand eight. Noah mixed up the place values in both periods.

- Read the display as one whole number. - Compare the part before “thousand” and the final part separately.

1. Eight hundred ten thousand one represents \(810{,}001\). 2. The display instead has \(801\) in the thousands period and \(010\) in the ones period. 3. The correct announcement is eight hundred one thousand ten.

eight hundred one thousand ten

- Convert each number name to standard form. - Pay close attention to the tens and ones places in the final period.

1. Two hundred thirty-eight thousand forty is \(238{,}040\), so the first pair is correct. 2. Six hundred thousand ninety is \(600{,}090\), not \(600{,}009\), so the second pair is incorrect. 3. Eight hundred twenty thousand is \(820{,}000\), and nine hundred forty-five thousand forty-five is \(945{,}045\), so the last two pairs are correct. 4. The correct name for \(600{,}009\) is six hundred thousand nine.

The pair \(600{,}009\) — six hundred thousand ninety is incorrect. The correct number name is six hundred thousand nine.

- Compare each stage with the stage immediately before it. - Convert both number names to standard form before deciding where the mismatch begins.

1. The slate \(904{,}004\) matches the narrator’s words, nine hundred four thousand four. 2. The caption nine hundred forty thousand four represents \(940{,}004\), so it does not match the earlier stages. 3. The first error occurs in the captions. 4. The correct caption is nine hundred four thousand four.

The first error occurs in the captions. The correct caption is nine hundred four thousand four.

- Convert both representations to the same form. - Compare the digits in every place.

1. The number \(709{,}090\) is read as seven hundred nine thousand ninety. 2. Seven hundred ninety thousand nine is \(790{,}009\). 3. Since \(709{,}090 \ne 790{,}009\), the claim is false.

The claim is false. \(709{,}090\) and \(790{,}009\) are different numbers.

- Build the thousands period first. - Then decide which card names the final two digits and which card does not match the numeral.

1. The thousands period \(926\) is formed by nine, hundred, and twenty-six. 2. The final period \(026\) is formed by twenty-six. 3. The complete number name is nine hundred twenty-six thousand twenty-six. 4. The card forty is not used.

nine hundred twenty-six thousand twenty-six; unused card: “forty”

- Write both possible numerals in word form. - Notice whether eight is part of the thousands period or comes after “thousand.”

1. Four hundred thousand eight has \(400\) in the thousands period and \(8\) in the ones period, so it is \(400{,}008\). Leah is correct. 2. The other numeral, \(408{,}000\), is read as four hundred eight thousand. 3. The two word forms show whether eight belongs in the thousands period or the ones period.

Leah is correct. \(400{,}008\) is four hundred thousand eight; \(408{,}000\) is four hundred eight thousand.

- Convert the incorrect label to standard form. - Compare the thousands period and final period separately with \(621{,}001\).

1. Six hundred twelve thousand ten represents \(612{,}010\), not \(621{,}001\). 2. The thousands period must be \(621\), read as six hundred twenty-one thousand. 3. The final period must be \(001\), read as one. 4. The correct number name is six hundred twenty-one thousand one.

The thousands period and the final period are both incorrect. The correct number name is six hundred twenty-one thousand one.

- Convert every entry to the same representation. - Compare the complete values only after all conversions are finished.

1. \(432{,}105\) is four hundred thirty-two thousand one hundred five. 2. Four hundred thirty-two thousand one hundred fifty is \(432{,}150\). 3. \(423{,}105\) and four hundred thirty-two thousand fifteen, or \(432{,}015\), are also different values. 4. The matching pair is \(432{,}105\) and four hundred thirty-two thousand one hundred five.

\(432{,}105\) and “four hundred thirty-two thousand one hundred five”

- Read each numeral completely in word form. - Pay close attention to the changing positions of \(3\), \(5\), and \(0\).

1. A: \(305{,}040\) is three hundred five thousand forty, so A matches II. 2. B: \(350{,}004\) is three hundred fifty thousand four, so B matches IV. 3. C: \(503{,}400\) is five hundred three thousand four hundred, so C matches I. 4. D: \(530{,}040\) is five hundred thirty thousand forty, so D matches III.

A: II B: IV C: I D: III

- Check each table row independently. - Convert a label to standard form if that makes the comparison easier.

1. North is correct: \(120{,}012\) is one hundred twenty thousand twelve. 2. South is incorrect. \(210{,}021\) is two hundred ten thousand twenty-one. 3. West is correct: \(102{,}210\) is one hundred two thousand two hundred ten. 4. East is incorrect. \(201{,}120\) is two hundred one thousand one hundred twenty.

South: two hundred ten thousand twenty-one. East: two hundred one thousand one hundred twenty.

- Convert each number name to standard form. - Check the final three digits in each pair.

1. For A, three hundred twenty-five thousand forty is \(325{,}040\), so the claim is correct. 2. For B, three hundred fifty-two thousand forty is \(352{,}040\), not \(352{,}400\). 3. The correct number name for \(352{,}400\) is three hundred fifty-two thousand four hundred.

A: Correct. B: Incorrect. The correct pair is \(352{,}400\) — three hundred fifty-two thousand four hundred.

- Begin with the representation that the problem identifies as correct. - Convert that announcement into both standard form and word form.

1. The announcement two hundred eighty-six thousand four hundred nineteen represents \(286{,}419\). 2. The display \(268{,}491\) is incorrect and must be changed to \(286{,}419\). 3. The printout also represents \(268{,}491\), so it must be changed to two hundred eighty-six thousand four hundred nineteen. 4. After both corrections, all three representations match.

Display: \(286{,}419\). Printout: two hundred eighty-six thousand four hundred nineteen.

- Check each pair independently instead of assuming the claim is true. - Read each numeral and each number name by periods.

1. The first pair is correct: six hundred eighteen thousand eighty is \(618{,}080\). 2. The second pair is incorrect. \(860{,}008\) is eight hundred sixty thousand eight. 3. The third pair is incorrect. \(806{,}800\) is eight hundred six thousand eight hundred. 4. Two pairs are incorrect, so the statement that exactly one pair is incorrect is false.

The claim is false. The correct pairs are \(618{,}080\) — six hundred eighteen thousand eighty; \(860{,}008\) — eight hundred sixty thousand eight; \(806{,}800\) — eight hundred six thousand eight hundred.