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3.2 Multiplying and dividing by powers of 10

3.2 Multiplying and dividing by powers of 10

Look at this section of the decimal place-value table.
… Thousands Hundreds Tens Units • tenths hundredths thousandths …
1 1 1
… 1000 100 10 1 s …
10 100 1000
!e numbers 10, 100, 1000, … can be written as powers of 10.
1
!e numbers , 1 , 1 , … can also can be written as powers of 10.
10 100 1000
Look at this pattern of numbers, written as powers of 10. Is there a link between the powers
and the value?
0 1
1
1
..., 1000 = 10 , 100 = 10 , 10 = 10 , 1 = 10 , 10 = 10 , 100 = 10 , 1000 = 10 , ...
−3
3
−1
−2
2
1
You should see that the decimal 0.1 can be written as or 10 .
1
−1
10
You can also see that the decimal 0.01 can be written as 1 or 10 .
−2
100
!is pattern continues as the numbers get bigger and smaller.
For example, 10 000 = 10 and 1 = 10 , 100 000 = 10 and 1 = 10 .
4
−4
−5
5
10000 100000
It is important to remember these two key points:
1
c Multiplying a number by , 1 , 1 , … is the same as dividing the same number
by 10, 100, 1000, … 10 100 1000
1
d Dividing a number by , 1 , 1 , … is the same as multiplying the same number
10 100 1000
by 10, 100, 1000, …
Worked example 3.2
4
3
−2
Work these out. a 2.5 × 10 b 12 × 10 c 365 ÷ 10 d 0.45 ÷ 10 −3
a 10 = 1000 Start by writing 10 as 1000.
3
3
2.5 × 1000 Rewrite the multiplication as 2.5 × 1000.
= 2500 Finally, work out the answer.
1
1
b 10 = 100 Start by writing 10 as 100 .
−2
−2
1
1
12 × 100 = 12 ÷ 100 Multiplying 12 by 100 is the same as dividing 12 by 100.
= 0.12 Finally, work out the answer.
c 10 = 10 000 Start by writing 10 as 10 000.
4
4
365 ÷ 10 000 Rewrite the division as 365 ÷ 10 000.
= 0.0365 Finally, work out the answer.
1
1
d 10 = 1000 Start by writing 10 as 1000 .
−3
−3
1
1
0.45 ÷ 1000 = 0.45 × 1000 Dividing 0.45 by 1000 is the same as multiplying 0.45 by 1000.
= 450 Finally, work out the answer.
26 3 Place value, ordering and rounding