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PLACE VALUE / DECIMALS

Multiplying decimals worksheets

Show tenths on a hundred grid, then use place value to multiply larger decimals. Print the student sheet and its worked key separately.

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Tenths on a hundred grid

4 questions · US Letter · separate answer key

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Tenths on a hundred grid · US Letter · Edition 0DKREUO. First problem: 0.6 × 0.4.

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Tenths on a hundred grid. Student sheet with 4 problems. First problem: 0.6 × 0.4.
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Mark two tenths factors on a 10-by-10 unit square. Count the overlap in hundredths.

  1. 0.6 × 0.4
  2. 0.6 × 0.5
  3. 0.2 × 0.7
  4. 0.4 × 0.2
Tenths on a hundred grid. Worked key with 4 problems. First problem: 0.6 × 0.4.
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Mark two tenths factors on a 10-by-10 unit square. Count the overlap in hundredths.

  1. 0.6 × 0.4 — 24 of 100 cells overlap. 6 × 4 = 24. Decimal places: 1 + 1 = 2. Product 0.24. 0.4 < 1, so the product is less than 0.6.
  2. 0.6 × 0.5 — 30 of 100 cells overlap. 6 × 5 = 30. Decimal places: 1 + 1 = 2. Product 0.30 = 0.3. 0.5 < 1, so the product is less than 0.6.
  3. 0.2 × 0.7 — 14 of 100 cells overlap. 2 × 7 = 14. Decimal places: 1 + 1 = 2. Product 0.14. 0.7 < 1, so the product is less than 0.2.
  4. 0.4 × 0.2 — 8 of 100 cells overlap. 4 × 2 = 8. Decimal places: 1 + 1 = 2. Product 0.08. 0.2 < 1, so the product is less than 0.4.

CHECK THE SAME PROBLEMS

0.6 × 0.4

Question 1 of 4

Unmarked grid on a unit square of 10 rows and 10 columns

FOUR PRACTICE SETS

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Tenths on a hundred grid

Mark two tenths factors on a 10-by-10 unit square. Count the overlap in hundredths.

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Tenths on a hundred grid student pageLook inside this original setStudent sheet and worked key
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Tenths on a hundred grid · US Letter · Edition 0DKREUO. First problem: 0.6 × 0.4.

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Tenths on a hundred grid. Student sheet with 4 problems. First problem: 0.6 × 0.4.
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Read questions as text

Mark two tenths factors on a 10-by-10 unit square. Count the overlap in hundredths.

  1. 0.6 × 0.4
  2. 0.6 × 0.5
  3. 0.2 × 0.7
  4. 0.4 × 0.2
Tenths on a hundred grid. Worked key with 4 problems. First problem: 0.6 × 0.4.
Download this worked key (PDF) ↓
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Mark two tenths factors on a 10-by-10 unit square. Count the overlap in hundredths.

  1. 0.6 × 0.4 — 24 of 100 cells overlap. 6 × 4 = 24. Decimal places: 1 + 1 = 2. Product 0.24. 0.4 < 1, so the product is less than 0.6.
  2. 0.6 × 0.5 — 30 of 100 cells overlap. 6 × 5 = 30. Decimal places: 1 + 1 = 2. Product 0.30 = 0.3. 0.5 < 1, so the product is less than 0.6.
  3. 0.2 × 0.7 — 14 of 100 cells overlap. 2 × 7 = 14. Decimal places: 1 + 1 = 2. Product 0.14. 0.7 < 1, so the product is less than 0.2.
  4. 0.4 × 0.2 — 8 of 100 cells overlap. 4 × 2 = 8. Decimal places: 1 + 1 = 2. Product 0.08. 0.2 < 1, so the product is less than 0.4.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Decimals × whole numbers

Multiply a decimal by a whole number and locate the product using place value.

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Decimals × whole numbers student pageLook inside this original setStudent sheet and worked key
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Decimals × whole numbers · US Letter · Edition 0CRICFE. First problem: 4 × 0.08.

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Decimals × whole numbers. Student sheet with 8 problems. First problem: 4 × 0.08.
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Multiply a decimal by a whole number and locate the product using place value.

  1. 4 × 0.08
  2. 6.3 × 8
  3. 3 × 0.54
  4. 4.2 × 8
  5. 7 × 0.06
  6. 6.0 × 6
  7. 5 × 0.75
  8. 1.8 × 8
Decimals × whole numbers. Worked key with 8 problems. First problem: 4 × 0.08.
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Multiply a decimal by a whole number and locate the product using place value.

  1. 4 × 0.08 — 4 × 8 = 32. Decimal places: 0 + 2 = 2. Product 0.32. 0.08 < 1, so the product is less than 4.
  2. 6.3 × 8 — 63 × 8 = 504. Decimal places: 1 + 0 = 1. Product 50.4. 8 > 1, so the product is greater than 6.3.
  3. 3 × 0.54 — 3 × 54 = 162. Decimal places: 0 + 2 = 2. Product 1.62. 0.54 < 1, so the product is less than 3.
  4. 4.2 × 8 — 42 × 8 = 336. Decimal places: 1 + 0 = 1. Product 33.6. 8 > 1, so the product is greater than 4.2.
  5. 7 × 0.06 — 7 × 6 = 42. Decimal places: 0 + 2 = 2. Product 0.42. 0.06 < 1, so the product is less than 7.
  6. 6.0 × 6 — 60 × 6 = 360. Decimal places: 1 + 0 = 1. Product 36.0 = 36. 6 > 1, so the product is greater than 6.0.
  7. 5 × 0.75 — 5 × 75 = 375. Decimal places: 0 + 2 = 2. Product 3.75. 0.75 < 1, so the product is less than 5.
  8. 1.8 × 8 — 18 × 8 = 144. Decimal places: 1 + 0 = 1. Product 14.4. 8 > 1, so the product is greater than 1.8.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Multiply two decimals

Use the whole-number calculation and then place the point. Includes tenths and hundredths in both factors.

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Multiply two decimals student pageLook inside this original setStudent sheet and worked key
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Multiply two decimals · US Letter · Edition 0M2BBBV. First problem: 1.2 × 0.35.

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Multiply two decimals. Student sheet with 8 problems. First problem: 1.2 × 0.35.
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Use the whole-number calculation and then place the point. Includes tenths and hundredths in both factors.

  1. 1.2 × 0.35
  2. 0.06 × 0.04
  3. 2.50 × 0.4
  4. 2.19 × 0.29
  5. 1.8 × 0.55
  6. 0.04 × 0.02
  7. 6.7 × 2.2
  8. 2.11 × 0.89
Multiply two decimals. Worked key with 8 problems. First problem: 1.2 × 0.35.
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Use the whole-number calculation and then place the point. Includes tenths and hundredths in both factors.

  1. 1.2 × 0.35 — 12 × 35 = 420. Decimal places: 1 + 2 = 3. Product 0.420 = 0.42. 0.35 < 1, so the product is less than 1.2.
  2. 0.06 × 0.04 — 6 × 4 = 24. Decimal places: 2 + 2 = 4. Product 0.0024. 0.04 < 1, so the product is less than 0.06.
  3. 2.50 × 0.4 — 250 × 4 = 1000. Decimal places: 2 + 1 = 3. Product 1.000 = 1. 0.4 < 1, so the product is less than 2.50.
  4. 2.19 × 0.29 — 219 × 29 = 6351. Decimal places: 2 + 2 = 4. Product 0.6351. 0.29 < 1, so the product is less than 2.19.
  5. 1.8 × 0.55 — 18 × 55 = 990. Decimal places: 1 + 2 = 3. Product 0.990 = 0.99. 0.55 < 1, so the product is less than 1.8.
  6. 0.04 × 0.02 — 4 × 2 = 8. Decimal places: 2 + 2 = 4. Product 0.0008. 0.02 < 1, so the product is less than 0.04.
  7. 6.7 × 2.2 — 67 × 22 = 1474. Decimal places: 1 + 1 = 2. Product 14.74. 2.2 > 1, so the product is greater than 6.7.
  8. 2.11 × 0.89 — 211 × 89 = 18779. Decimal places: 2 + 2 = 4. Product 1.8779. 0.89 < 1, so the product is less than 2.11.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

Decimals × 10, 100 or 1,000

Follow the value of each digit when multiplying by a power of ten.

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Decimals × 10, 100 or 1,000 student pageLook inside this original setStudent sheet and worked key
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Decimals × 10, 100 or 1,000 · US Letter · Edition 1C6IBQJ. First problem: 0.06 × 100.

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Decimals × 10, 100 or 1,000. Student sheet with 8 problems. First problem: 0.06 × 100.
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Follow the value of each digit when multiplying by a power of ten.

  1. 0.06 × 100
  2. 17.8 × 10
  3. 0.58 × 1000
  4. 10.7 × 100
  5. 1.89 × 10
  6. 16.7 × 1000
  7. 1.41 × 100
  8. 2.7 × 10
Decimals × 10, 100 or 1,000. Worked key with 8 problems. First problem: 0.06 × 100.
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Follow the value of each digit when multiplying by a power of ten.

  1. 0.06 × 100 — 6 × 100 = 600. Decimal places: 2 + 0 = 2. Product 6.00 = 6. Each digit moves 2 places left.
  2. 17.8 × 10 — 178 × 10 = 1780. Decimal places: 1 + 0 = 1. Product 178.0 = 178. Each digit moves 1 place left.
  3. 0.58 × 1000 — 58 × 1000 = 58000. Decimal places: 2 + 0 = 2. Product 580.00 = 580. Each digit moves 3 places left.
  4. 10.7 × 100 — 107 × 100 = 10700. Decimal places: 1 + 0 = 1. Product 1070.0 = 1070. Each digit moves 2 places left.
  5. 1.89 × 10 — 189 × 10 = 1890. Decimal places: 2 + 0 = 2. Product 18.90 = 18.9. Each digit moves 1 place left.
  6. 16.7 × 1000 — 167 × 1000 = 167000. Decimal places: 1 + 0 = 1. Product 16700.0 = 16700. Each digit moves 3 places left.
  7. 1.41 × 100 — 141 × 100 = 14100. Decimal places: 2 + 0 = 2. Product 141.00 = 141. Each digit moves 2 places left.
  8. 2.7 × 10 — 27 × 10 = 270. Decimal places: 1 + 0 = 1. Product 27.0 = 27. Each digit moves 1 place left.
Original PDFs · Letter and A4

US Letter · Student / Key / Both

A4 · Student / Key / Both

AT THE MARKING TABLE

Are the digits wrong, or is the value wrong?

For 0.6 × 0.4, mark six rows and four columns of a hundred grid. The overlap covers 24 cells, each worth 0.01. It represents 0.24 of the whole. Since 0.4 is less than one, the product must be smaller than 0.6.

For 1.2 × 0.35, the whole-number calculation is 12 × 35 = 420. One decimal place plus two gives three places before trimming. Write 0.420. The shorter form 0.42 has the same value. If a learner writes 4.2, inspect the whole-number step before deciding what to reteach.

Multiplying 0.06 by 100 makes each digit worth one hundred times as much. Six hundredths become six ones. Compare that with 0.06 × 0.04, where four decimal places are needed to write 0.0024.

The tenths models and whole-number sets practise selected place-value work in Common Core 5.NBT.B.7. The two-decimal set extends to products in thousandths and ten-thousandths. For another view of the same area, try multiplying fractions. For larger whole numbers, use three-digit multiplication.

Use the DC1 code on a printed sheet in Find my worksheet. For a mixed check, open the fifth grade multiplication guide. Original decimal sets can also be combined in a worksheet packet.

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