STRAND: Number
TOPIC:
Decimal numbers
Multiplying and dividing by powers
of 10 (10, 100, 1000 and so on)
To multiply a whole number by a power of 10, add as many zeros to that number as there are in the power of 10. For example,
to multiply by 10, add one zero and to multiply by 100, add two zeros.
To multiply a decimal number by a power of 10, move the decimal point to the right one place for each zero in the power of
10. For example, to multiply by 10 move the decimal point one place to the right, while to multiply by 1000 move it three
places to the right. Note that if there are not enough digits after the decimal point, we can always add extra zeros.
WORKED Example 1
Calculate each of the following.
a 72 × 10
b 540 × 1000
c 5.67 × 10
d 0.7 × 100
THINK
WRITE
a To multiply a whole number by 10, add one 0
to the number, as there is only one zero in 10.
a 72 × 10 = 720
b To multiply a whole number by 1000, add
three zeros, since there are 3 zeros in 1000.
b 540 × 1000 = 540 000
c To multiply a decimal number by 10, move the
decimal point one place to the right (as there is
one zero in 10).
c 5.67 × 10 = 56.7
d To multiply a decimal number by 100, we need
to move the decimal point two places to the
right. However there is only one digit after the
decimal point (7). So add a zero first (to create
two decimal places), then move the decimal
point. Note that we write the answer as 70,
rather than 070.
d 0.7 × 100
= 0.70 × 100
= 70
To divide a whole or a decimal number by a power of 10, move the decimal point to the left one place for each zero in the
power of 10. Note that although a whole number does not have a decimal point, we can always add it at the end of the number.
(For example, 35 and 35 are the same numbers.) Also note that if there are not enough digits to move the decimal point the
required number of places, we can always add extra zeros.
 John Wiley & Sons Australia, Ltd 2001
SKILLBUILDER: Multiplying and
dividing by powers of 10
(10, 100, 1000 and so on)
STRAND: Number
TOPIC:
Decimal numbers
WORKED Example 2
Calculate each of the following.
a 234 ÷ 100
b 350 ÷ 1000
c 75.6 ÷ 10
d 4.1 ÷ 1000
THINK
WRITE
a
Put a decimal point at the end of the whole
number.
To divide by 100, move the decimal point 2
places to the left, as there are 2 zeros in
100.
a 234 ÷ 100 = 234. ÷ 100
Put a decimal point at the end of the whole
number.
There are 3 zeros in 1000, so to divide by
1000 move the decimal point 3 places to
the left. You may wish to rewrite your
answer, omitting the zero at the end of the
resulting decimal (as 0.350 = 0.35).
b 350 ÷ 1000 = 350. ÷ 1000
1
2
b
1
2
234 ÷ 100 = 2.34
234 ÷ 1 00 = 0.350
234 ÷ 100 = 0.35
c To divide by 10, move the decimal point one
place to the left (as there is 1 zero in 10).
c 75.6 ÷ 10 = 7.56
d To divide by 1000, move the decimal point 3
places to the left, since there are 3 zeros in
1000. (Add two extra zeros in front of the
number 4.)
d 4.1 ÷ 1000 = 0.0041
Try these
1 Calculate each of the following.
a 23 × 10
b 45 × 10
e 2500 × 10
f 71 × 100
i 25 × 1000
j 710 × 1000
c 235 × 10
g 531 × 100
k 2 × 10 000
d 530 × 10
h 300 × 100
l 70 × 10 000
2 Calculate each of the following.
a 2.56 × 10
b 7.6 × 10
e 2.6 × 100
f 70.1 × 100
i 10.2 × 1000
j 0.758 × 1000
c 0.98 × 10
g 0.2 × 100
k 2.5 × 10 000
d 3.49 × 100
h 5.321 × 1000
l 3.576 × 10 000
3 Calculate each of the following.
a 128 ÷ 10
b 7560 ÷ 10
e 15 ÷ 100
f 7 ÷ 100
i 3 ÷ 1000
j 75 ÷ 1000
c 3400 ÷ 10
g 560 ÷ 100
k 600 ÷ 1000
d 2050 ÷ 10
h 7210 ÷ 100
l 2500 ÷ 10 000
4 Calculate each of the following.
a 9.2 ÷ 10
b 52.3 ÷ 10
e 4.9 ÷ 100
f 123.4 ÷ 100
i 155.6 ÷ 1000 j 4.25 ÷ 1000
c 0.5 ÷ 10
g 0.3 ÷ 100
k 75.3 ÷ 10 000
d 8.19 ÷ 100
h 71.1 ÷ 1000
l 1000.5 ÷ 10 000
 John Wiley & Sons Australia, Ltd 2001