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 http://www.themathpage.com/arith/powers-of-10.htm

Number Ten (10) Number Ten (10) is a collection of ten Ones.   10 = 10 x 1 http://www.themathpage.com/arith/powers-of-10.htm

Number One Hundred (100) One Hundred (100) is a collection of ten Tens. 100 = 10 x 10 http://www.themathpage.com/arith/powers-of-10.htm

Number One Thousand (1 000) One Thousand (1000) is a collection of ten One Hundreds 10 x 100    http://www.themathpage.com/arith/powers-of-10.htm

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 http://www.themathpage.com/arith/powers-of-10.htm

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 0.00001 1/100 000   One Millionth 0.000001 1/1 000 000 http://www.themathpage.com/arith/powers-of-10.htm

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

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)

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!

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

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

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

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

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: ??

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

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

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

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

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) http://www.themathpage.com/arith/multiply-by-powers-of-10-2.htm

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!

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

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

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

PRACTICE Divide a) 365 ÷ 10 b) 365 ÷ 100 c) 365 ÷ 1000 d) 8970 ÷ 0.1 f) 8970 ÷ 0.001

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