Exponents and Powers of 10 Worksheets

Pick a sheet, press Make a new sheet for new numbers, and print it with the answer key.

20 problems. Multiply whole numbers by 10, 100 and 1,000. Sheet 5H2NIF, with its answer key.

Multiply whole numbers by 10, 100 and 1,000

Name Date Score / 20

Multiply. The digits stay the same: each moves one place for every zero.

  1. 1.169 × 100 = ________
  2. 2.984 × 100 = ________
  3. 3.839 × 1,000 = ________
  4. 4.36 × 10 = ________
  5. 5.40 × 1,000 = ________
  6. 6.336 × 10 = ________
  7. 7.275 × 10 = ________
  8. 8.505 × 1,000 = ________
  9. 9.122 × 10 = ________
  10. 10.287 × 1,000 = ________
  11. 11.838 × 1,000 = ________
  12. 12.731 × 100 = ________
  13. 13.942 × 1,000 = ________
  14. 14.829 × 100 = ________
  15. 15.924 × 10 = ________
  16. 16.706 × 1,000 = ________
  17. 17.349 × 100 = ________
  18. 18.714 × 100 = ________
  19. 19.188 × 100 = ________
  20. 20.893 × 10 = ________

Sheet 5H2NIF · Made at homeroomtools.com

Answer key. Multiply whole numbers by 10, 100 and 1,000

  1. 1.169 × 100 = 16,9002 places to the left
  2. 2.984 × 100 = 98,4002 places to the left
  3. 3.839 × 1,000 = 839,0003 places to the left
  4. 4.36 × 10 = 3601 place to the left
  5. 5.40 × 1,000 = 40,0003 places to the left
  6. 6.336 × 10 = 3,3601 place to the left
  7. 7.275 × 10 = 2,7501 place to the left
  8. 8.505 × 1,000 = 505,0003 places to the left
  9. 9.122 × 10 = 1,2201 place to the left
  10. 10.287 × 1,000 = 287,0003 places to the left
  11. 11.838 × 1,000 = 838,0003 places to the left
  12. 12.731 × 100 = 73,1002 places to the left
  13. 13.942 × 1,000 = 942,0003 places to the left
  14. 14.829 × 100 = 82,9002 places to the left
  15. 15.924 × 10 = 9,2401 place to the left
  16. 16.706 × 1,000 = 706,0003 places to the left
  17. 17.349 × 100 = 34,9002 places to the left
  18. 18.714 × 100 = 71,4002 places to the left
  19. 19.188 × 100 = 18,8002 places to the left
  20. 20.893 × 10 = 8,9301 place to the left

Sheet 5H2NIF · Made at homeroomtools.com

Next step Practise the times tables behind the zerosPrint a place value chart

How it works

Free exponents and powers of 10 worksheets move digits: multiply or divide whole numbers and decimals by 10, 100 and 1,000, then by 10¹ to 10⁵. The key says how many places each answer moved.

Read the full guide

Count the places

Each zero of 10, 100 or 1,000 moves the digits one place: 47 × 100 = 4,700, two places left. Dividing moves them right, past the point when needed: 4.7 ÷ 100 = 0.047. The first sheets use whole numbers, then decimals.

Exponents

In 10³ the exponent 3 is the number of zeros, so 10³ = 1,000 and the digits move 3 places. Powers of ten written both ways mixes 1,000 and 10³ on one sheet, so pupils see they are one number.

  • Say 'the digits move', not 'the point moves' or 'add a zero': 3.25 × 10 is 32.5, and adding a zero would give 3.250.
  • Go in the order of the menu: whole numbers, then decimals, then exponents. The rule stays the same; only the numbers get harder.

Questions and answers

What grade learns powers of 10?

In Common Core states, grade 5 explains the pattern of zeros and of the decimal point when multiplying or dividing by powers of 10, and writes powers of 10 with whole-number exponents.

What is 10 to the power of 3?

10³ is 10 × 10 × 10 = 1,000. The exponent counts the tens multiplied together, which is also the number of zeros after the 1.

Why does dividing by 0.1 make a number bigger?

0.1 fits into 1 ten times, so dividing by 0.1 is the same as multiplying by 10: 8 ÷ 0.1 = 80. One sheet has pupils write that matching multiplication under each division.

All 11 sheet types

Whole numbers 3

  • Divide whole numbers by 10, 100 and 1,000 3,600 ÷ 100 = 36, and 36 ÷ 100 = 0.36: the digits move right, past the point when they must.
  • Multiply or divide whole numbers by 10, 100, 1,000 Half the problems multiply and half divide, so the pupil reads the sign first: 52 × 10 = 520, 52 ÷ 10 = 5.2.
  • Multiply whole numbers by 10, 100 and 1,000 47 × 100 = 4,700: each digit moves two places to the left, and zeros fill the empty places.

Decimals 4

  • Divide by 0.1 or 0.01, then write the multiplication 8 ÷ 0.01 = 800, and so does 8 × 100: two lines for each problem.
  • Divide decimals by 10, 100 and 1,000 4.7 ÷ 100 = 0.047: zeros go in front to hold the places.
  • Multiply and divide decimals by 0.1 and 0.01 Multiplying by 0.1 is dividing by 10: 36 × 0.1 = 3.6. Dividing by 0.01 is multiplying by 100: 0.8 ÷ 0.01 = 80.
  • Multiply decimals by 10, 100 and 1,000 3.25 × 100 = 325: two places to the left, so the point moves past both digits after it.

Exponents 4

  • Divide by 10¹, 10² and 10³ 52 ÷ 10³ = 0.052: three places to the right.
  • Multiply by 10¹, 10² and 10³ 6.4 × 10² = 640: the exponent is the number of places the digits move, 2 here.
  • Multiply or divide by 10¹ to 10⁵ 0.37 × 10⁵ = 37,000 and 81 ÷ 10⁴ = 0.0081: bigger exponents, the same rule.
  • Powers of ten written both ways Half the problems show 1,000 and half show 10³, so the pupil sees they are the same number.

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