Multiply and Divide Decimals by Powers of 10

Multiply and Divide Decimals by Powers of 10 Mrs. Young EMC 1

What are powers of 10? ? ? • 1, 100, 10000, etc. are all powers of 10 • These numbers can be written using exponents • 1 = 10 0 • 10 = 10 1 2 • 100 = 10 3 • 1000 = 10 4 • 10000 = 10

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

Powers of 10 continued… • The fractions , , etc… are also considered powers of ten. – In decimal form they can be written 0. 1, 0. 001, 0. 0001, etc.

Powers of 10 practice 1) Of the following ten decimal numbers, five are powers of 10. • Circle them. 1, 000 100. 1 0. 0011 1 0. 00001 20, 000 0. 010 1, 100 0

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 x 10 = 12. 5 100 = 125 1, 000 = 1, 250, 000

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 1 (move decimal to right once) 1. 25 x 10 2 (move decimal to right two times) 1. 25 x 10 3 (move decimal to right three times) 6 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

Multiply by Powers of 10 Do some by yourself. • 3. 8 x 10 = _____ 3 • 3. 8 x 10 = _____ 7 • 3. 8 x 10 = _____ • 3. 8 x 10, 000 = _____

More difficult examples • 1, 280 x 1, 000 = 1, 280, 000 2 • 0. 026 x 10 = 2. 6 • 10. 0036 x 1, 000 = 10, 003. 6 4 • 4. 99 x 10 = 49, 900

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 4 250. 6 ÷ 10 = 0. 02506 6 250. 6 ÷ 10 = 0. 0002506

Dividing by Powers of 10 • Do some by yourself. 4 375 ÷ 10 = _____ 0 375 ÷ 10 = _____ 375 ÷ 100 = _____ 9 375 ÷ 10 = _____

More difficult examples • 7. 25 ÷ 1, 000 = 0. 00725 • 0. 036 ÷ 10 = 0. 0036 2 • 360, 000 ÷ 10 = 3, 600 • 4, 500 ÷ 10, 000 = 0. 45