Multiply and Divide Decimals by Powers of 10

What are powers of 10??? 1, 10, 100, 1000, 10000, etc. are all powers of 10 These numbers can be written using exponents 1 = 10 10 = 10 100 = 10 1000 = 10 10000 = 10 1 2 3 4

What are exponents? An exponent tells us how many times to multiply a number by itself For example 10 This tells us to multiply 10 x 10 5 This tells us to multiply 5 x 5 x 5 2 3

Powers of 10 continued… The fractions etc… are also considered powers of ten. In decimal form they can be written 0.1, 0.01, 0.001, 0.0001, etc.

Multiplying by powers of 10 Probably because we have ten fingers, we use a decimal system which is based on powers of 10. Because of this, it is easy to multiply and divide by powers of 10. To do so we only need to move the decimal place.

Multiply by Powers of 10 To multiply a number by a power of 10 like 10, 100, or 1000, we just have to move the decimal point to the right an appropriate number of places. To multiply by 10 we move one place To multiply by 100 we move two places To multiply by 1000 we move three places and so on.

Multiply by Powers of 10 Here are some examples: 1.25 x 10 = 12.5

Multiply by Powers of 10 using exponents With the same examples as the previous slide, we can use exponents to multiply by powers of 10 1.25 x 10 (move decimal to right once) 1.25 x 10 (move decimal to right two times) 1.25 x 10 (move decimal to right three times) 1.25 x 10 (move decimal to right six times) **The exponent tells us how many times to move the decimal point to the right 1 2 3 6

Multiply by Powers of 10 Do some by yourself. 3.8 x 10 = __________ 7

More difficult examples 2 4

Dividing by powers of 10 Dividing is just as easy; the decimal place simply moves to the left instead of to the right. 250.6 ÷ 10 = 25.06 250.6 ÷ 100 = 2.506 250.6 ÷ 10 = 0.02506 250.6 ÷ 10 = 0.0002506 4 6

Dividing by Powers of 10 Do some by yourself. 375 ÷ 10 = __________ 375 ÷ 10 = __________ 375 ÷ 100 = __________ 4 9

More difficult examples 7.25 ÷ 1,000 = 0.00725 0.036 ÷ 10 = 0.0036 360,000 ÷ 10 = 3,600 4,500 ÷ 10,000 = 0.45 2