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POWERS OF TEN

POWERS OF TEN. Which Numbers are The Powers of 10 ?. are the numbers produced when, starting with one (1), and repeatedly collect them into groups of 10 . 1, 10, 100 etc 0.1, 0.01, 0.001 etc. Number Ten (10). Number Ten (10) is a collection of ten Ones.   10 = 10 x 1.

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POWERS OF TEN

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  1. POWERS OF TEN

  2. Which Numbers are The Powers of 10? • are the numbers produced when, starting with one (1), and repeatedly collect them into groups of 10. • 1, 10, 100 etc • 0.1, 0.01, 0.001 etc

  3. Number Ten (10) • Number Ten (10) is a collection of ten Ones. •   10 = 10 x 1

  4. Number One Hundred (100) • One Hundred (100) is a collection of ten Tens. • 100 = 10 x 10

  5. Number One Thousand (1 000) • One Thousand (1000) is a collection of ten One Hundreds • 10 x 100

  6. The Powers of 10 The Whole POWERS OF TEN

  7. The Decimal POWERS OF TEN

  8. How To Multiply a Number By a Whole Power of 10? • Add a place for as many zeroes as appear in the power • The decimal moves as many places to the RIGHT as there are zeroes • Remember multiplying a whole number by a whole number means the answer should be bigger! • 89 x 10 =89. x 10 = 890. • Decimal moves to the right one place

  9. How To Multiply a Number By a Whole Power of 10? Examples 36 × 10 = 360 Add on one 0. (1 place) 36 x 100 = 3600 Add on two 0's. (2 places) 36 x 1000 = 36 000 Add on three 0's. (3 places)

  10. How To Multiply a Number By a Decimal Power of 10? • Take a place away for each place past the decimal until a whole number is reached • e.g. 0.01 means move 2 places • 0.01 moves 2 places to the right to get 1 • ** Remember multiplying a decimal number by a whole number means the answer should be getting smaller!

  11. How To Multiply a Number By a Decimal Power of 10? Examples 3400 x 0.001 = 3400 = 3.400 = 3.4 3400 x 0.01 = 3400 = 34.00 = 34 3400 x 0.1 = 3400 = 340.0 = 340 The decimal in the whole number moves as many places to the LEFT

  12. How To Multiply a Number By a Decimal Power of 10? • Or move the decimal to the LEFT for each zero in the denominator • e.g. 0.01 is equal to 1/100 and there are two zeroes in the denominator • 0.1 = 1/10 1 zero = 1 place to the LEFT • 0.01 = 1/100 2 zeroes = 2 places to the LEFT • 0.001 = 1/1000 3 zeroes = 3 places to the LEFT • 0.0001 = 1/10 000 4 zeroes = 4 places to the LEFT

  13. How To Multiply a Number By a Decimal Power of 10? Examples 3400 x 0.001 = 3400 x 1/1000= 3.400 = 3.4 (3 places) 3400 x 0.01 = 3400 x 1/100 = 34.00 = 34 (2 places) 3400 x 0.1 = 3400 x 1/10 = 340.0 = 340 (1 place) The decimal in the whole number moves as many places to the LEFT

  14. PRACTICE Find the product. Write the rule for multiplying by 100. a) 100 x 350 b) 100 x 35 c) 100 x 3.5 d) 100 x 0.35 e) 679 x 100 f) 67.9 x 100 g) 6.79 x100 h) 0.679 x 100

  15. PRACTICE Find the product. Write the rule for multiplying by 100. a) 100 x 350 = 350 000 b) 100 x 35 = 3 500 c) 100 x 3.5 = 350 d) 100 x 0.35 = 35 e) 679 x 100 = 679 000 f) 67.9 x 100 = 6 790 g) 6.79 x100 = 679 h) 0.679 x 100 = 67.9 Rule: ??

  16. PRACTICE Find the product. Write the rule for multiplying by 100. a) 100 x 350 = 350 000 b) 100 x 35 = 3 500 c) 100 x 3.5 = 350 d) 100 x 0.35 = 35 e) 679 x 100 = 679 000 f) 67.9 x 100 = 6 790 g) 6.79 x100 = 679 h) 0.679 x 100 = 67.9 Rule: When Multiplying by 100 move decimal 2 places to the Right

  17. PRACTICE • Multiply the following • a) 234 x 100 • b) 0.01 x 29 • c) 300 x 0.1 • d) 45.7 x1000 • e) 10 x 4.3 • f) 0.001 x 600 • g) 0.1 x 56.3 • h) 1000 x 8300

  18. PRACTICE • Multiply the following • a) 234 x 100 = 23 400 • b) 0.01 x 29 = 0.29 • c) 300 x 0.1 = 30 • d) 45.7 x1000 = 45 700 • e) 10 x 4.3 = 43 • f) 0.001 x 600 = 0.6 • g) 0.1 x 56.3 = 5.63 • h) 1000 x 8300 = 8 300 000

  19. How To Divide a Number By a Whole Power of 10? • take away a place for as many zeroes as appear in the power • The decimal moves as many places to the LEFT as there are zeroes • Remember dividing a whole number by a whole number means the answer should be smaller! • 89 ÷ 10 =89. ÷ 10 = 8.9 • Decimal moves to the left one place

  20. How To Divide a Number By a Whole Power of 10? Examples 36 ÷ 10 = 3.6 Take away 1 place (one 0) 36 / 100 = 0.36 Take away 2 place (two 0) 36 ÷ 1000 = 0.036 Take away 3 place (three 0)

  21. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN • Add a place for each place past the decimal until a whole number is reached • e.g. 0.01 means move 2 places • 0.01 moves 2 places to the right to get 1 • ** Remember dividing a whole number by a decimal means the answer should be getting bigger!

  22. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN Examples 3400 ÷ 0.001 = 3 400 000 3400 / 0.01 = 340 000 3400 ÷ 0.1 = 34 000 The decimal in the whole number moves as many places to the RIGHT

  23. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN • Or move the decimal to the RIGHT for each zero in the denominator • e.g. 0.01 is equal to 1/100 and there are two zeroes in the denominator • 0.1 = 1/10 1 zero = 1 place to the RIGHT • 0.01 = 1/100 2 zero = 2 place to the RIGHT • 0.001 = 1/1000 3 zeroes = 3 place to the RIGHT • 0.0001 = 1/10 000 4 zeroes = 4 place to the RIGHT

  24. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN Examples 3400 / 0.001 = 3400 ÷ 1/1000= 3 400 000 (3 places) 3400 ÷ 0.01 = 3400 ÷ 1/100 = 340 000(2 places) 3400 ÷ 0.1 = 3400 ÷ 1/10 = 34 000 (1 place) The decimal in the whole number moves as many places to the RIGHT

  25. PRACTICE Divide a)365 ÷ 10 b) 365 ÷ 100 c) 365 ÷ 1000 • d) 8970 ÷ 0.1 • e) 8970 ÷ 0.01 • f) 8970 ÷ 0.001

  26. PRACTICE Divide • 365 ÷ 10 = 36.5 • 365 ÷ 100 = 3.65 • 365÷ 1000 = 0.365 • 8970 ÷ 0.1 = 89 700 • 8970 ÷ 0.01 = 897 000 • 8970 ÷ 0.001 = 8 970 000

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