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 0
• 10 = 101
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 x 5
Powers of 10
continued…
• The fractions 1
10
1
100
1
1000
1
10000
etc… are also considered
powers of ten.
– In decimal form they can be
written 0.1, 0.01, 0.001, 0.0001,
etc.
Powers of 10 practice
1) Of the following ten decimal
numbers, five are powers of 10.
1,000,000
10.0
100.1
0.0011
20,000
1,100
1
0.00001
0.010
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
1.25
1.25
1.25
x
x
x
x
10 = 12.5
100 = 125
1,000 = 1,250
1,000,000 = 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