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POWERS OF TEN

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**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, etc

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**Number Ten (10) Number Ten (10) is a collection of ten Ones.**

10 = 10 x 1

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

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

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**The Whole POWERS OF TEN One 1 Ten 10 One hundred 100 One thousand**

The Powers of 10 The Whole POWERS OF TEN One 1 Ten 10 One hundred 100 One thousand 1,000 Ten thousand 10,000 One hundred thousand 100,000 One million 1,000,000 Ten million 10,000,000 One hundred million 100,000,000 One billion 1,000,000,000 Ten billion 10,000,000,000 One hundred billion 100,000,000,000

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**The Decimal POWERS OF TEN**

One Tenth 0.1 1/10 One Hundredth 0.01 1/100 One Thousandth 0.001 1/1000 One Ten Thousandth 0.0001 1/10 000 One Hundred Thousandth 1/ One Millionth 1/

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**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

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**How To Multiply a Number By a Whole Power of 10?**

Examples 36 × 10 = Add on one 0. (1 place) 36 x 100 = Add on two 0's. (2 places) 36 x 1000 = Add on three 0's. (3 places)

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**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 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!

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**How To Multiply a Number By a Decimal Power of 10?**

Examples 3400 x = = = 3.4 3400 x 0.01 = = = 34 3400 x 0.1 = = = 340 The decimal in the whole number moves as many places to the LEFT

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**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 is equal to 1/ and there are two zeroes in the denominator = 1/ zero = 1 place to the LEFT = 1/ zeroes = 2 places to the LEFT = 1/ zeroes = 3 places to the LEFT = 1/ zeroes = 4 places to the LEFT

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**How To Multiply a Number By a Decimal Power of 10?**

Examples 3400 x = 3400 x 1/1000= = 3.4 (3 places) 3400 x 0.01 = x 1/100 = = (2 places) 3400 x = 3400 x 1/10 = = 340 (1 place) The decimal in the whole number moves as many places to the LEFT

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**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) x 100

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**PRACTICE Find the product. Write the rule for multiplying by 100.**

a) 100 x = b) 100 x = 3 500 c) 100 x = 350 d) 100 x = 35 e) 679 x = f) 67.9 x = 6 790 g) 6.79 x = 679 h) x = 67.9 Rule: ??

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**PRACTICE Find the product. Write the rule for multiplying by 100.**

a) 100 x = b) 100 x = 3 500 c) 100 x = 350 d) 100 x = 35 e) 679 x = f) 67.9 x = 6 790 g) 6.79 x = 679 h) x = 67.9 Rule: When Multiplying by 100 move decimal 2 places to the Right

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**PRACTICE Multiply the following a) 234 x 100 b) 0.01 x 29 c) 300 x 0.1**

d) x1000 e) 10 x 4.3 f) x 600 g) 0.1 x 56.3 h) x 8300

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**PRACTICE Multiply the following a) 234 x 100 = 23 400**

b) x = 0.29 c) 300 x = 30 d) x = e) 10 x = 43 f) x = 0.6 g) 0.1 x = 5.63 h) x =

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**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

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**How To Divide a Number By a Whole Power of 10?**

Examples 36 ÷ 10 = Take away 1 place (one 0) 36 / 100 = Take away 2 place (two 0) 36 ÷ 1000 = Take away 3 place (three 0)

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**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 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!

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**HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN**

Examples 3400 ÷ = 3400 / 0.01 = 3400 ÷ 0.1 = The decimal in the whole number moves as many places to the RIGHT

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**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 is equal to 1/ and there are two zeroes in the denominator = 1/ zero = 1 place to the RIGHT = 1/ zero = 2 place to the RIGHT = 1/ zeroes = 3 place to the RIGHT = 1/ zeroes = 4 place to the RIGHT

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**HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN**

Examples 3400 / = 3400 ÷ 1/1000= (3 places) 3400 ÷ 0.01 = ÷ 1/100 = (2 places) 3400 ÷ = 3400 ÷ 1/10 = (1 place) The decimal in the whole number moves as many places to the RIGHT

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**PRACTICE Divide a) 365 ÷ 10 b) 365 ÷ 100 c) 365 ÷ 1000 d) 8970 ÷ 0.1**

f) 8970 ÷ 0.001

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**PRACTICE Divide 365 ÷ 10 = 36.5 365 ÷ 100 = 3.65 365÷ 1000 = 0.365**

365÷ = 0.365 8970 ÷ 0.1 = 8970 ÷ 0.01 = 8970 ÷ =

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