1) Powers of 10 refer to numbers like 1, 10, 100, 1000 that are 10 multiplied by itself a certain number of times, represented by exponents. 2) To multiply a number by a power of 10, move the decimal point to the right by the number of places represented by the exponent. To divide, move the decimal point left by the same number of places. 3) Examples demonstrate multiplying and dividing numbers by powers of 10 by moving the decimal point and using exponents to represent powers of 10.

1. Multiply and Divide
Decimals by
Powers of 10

2. • 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
What are powers of
10???
4
1
2
3
0

3. 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

4. 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.
1
10
1
100
1
1000
1
10000

5. 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.

6. Multiply by Powers of
10
• Here are some examples:
1.25 x 10 = 12.5
1.25 x 100 = 125
1.25 x 1,000 = 1,250
1.25 x 1,000,000 = 1,250,000

7. 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

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

9. More difficult examples
• 1,280 x 1,000 = 1,280,000
• 0.026 x 10 = 2.6
• 10.0036 x 1,000 = 10,003.6
• 4.99 x 10 = 49,900
2
4

10. 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

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

12. 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