Transcript Multiply and Divide Decimals by Powers of 10

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 = 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
• 10
• This tells us to multiply 10 x 10
•5 2
• This tells us to multiply 5 x 5 x 5
3
Powers of 10
continued…
• The fractions
,1
,1
, 1
, 1
10 100 1000 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.
• Circle them.
1,000,000
10.0
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
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 = __________
• 3.8 x 10 3= __________
• 3.8 x 10 =
7 __________
• 3.8 x 10,000 = __________
More difficult examples
• 1,280 x 1,000 = 1,280,000
• 0.026 x 10 =2 2.6
• 10.0036 x 1,000 = 10,003.6
• 4.99 x 10 = 49,900
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 =40.0002506
6
Dividing by
Powers of 10
• Do some by yourself.
375 ÷ 104= __________
375 ÷ 100 = __________
375 ÷ 100 = __________
375 ÷ 109 = __________
More difficult examples
• 7.25 ÷ 1,000 = 0.00725
• 0.036 ÷ 10 = 0.0036
• 360,000 ÷ 10 = 3,600
2
• 4,500 ÷ 10,000 = 0.45