number AND algebra • real numbers
Dividing a decimal number by another
decimal number
■■
A visual representation of 2.724 ó 0.4 is shown below.
2.724
0.4
0.4
0.4
0.4
0.4
0.4
0.4
2.724 ó 0.4 can be interpreted as ‘how many times does 0.4 divide into 2.724?’
2.724 ó 0.4 = 6.81
■■
When dividing one decimal by another,
multiply the decimal you are dividing by
(divisor) by a power of 10 to make it a
whole number. Multiply the other decimal
by the same power of 10, as shown at right.
This is the same as writing an equivalent
fraction with a whole number as the
ì 10
= 274.24 .
denominator: 2.0724
.4
10
First multiply this number by 10
to make a whole number.
Then multiply this
number by 10 also.
2.724 ó 0.4
Worked Example 27
Calculate: a 26.724 ó 0.4 b 3.0276 ó 0.12.
Think
a
1
Rewrite the question as a fraction.
2
Multiply both the numerator and the
denominator by the appropriate multiple of 10.
Write
a
26.724
0.4
26.724 10
=
×
0.4
10
26.724 ó 0.4 =
3
Divide the decimal by the whole number.
=
)
267.24
4
6 6 . 81
4 262 7.3 24
b
4
Write the answer.
1
Rewrite the question as a fraction.
2
Multiply both the numerator and the
denominator by the appropriate multiple of 10.
26.724 ó 0.4 = 66.81
b
3.0276
0.12
3.0276 100
=
×
0.12
100
3.0276 ó 0.12 =
3
Divide the decimal by the whole number.
=
)
302.76
12
2 5. 2 3
12 306 2.2 736
4
Write the answer.
3.0276 ó 0.12 = 25.23
Chapter 6 Decimals
209
nuMber AnD AlgebrA • real numbers
WorkeD exAMple 28
How many litres of petrol could be purchased for $50.88 if 1 litre costs $1.06?
Think
WriTe
1
Write the problem.
2
Rewrite the problem as a fraction.
3
Multiply the numerator and denominator by
the appropriate multiple of 10, in this case
100. Alternatively, the decimal point could
be moved twice to the right in both numbers
so that the divisor is a whole number (that is,
50.88 ó 1.06 = 5088 ó 106).
4
Divide the decimal by the whole number.
50.88 ó 1.06
50.88
=
1.06
50.88 100
=
×
1.06
100
5088
=
106
4 8
= 106 508848
)
50.88 ó 1.06 = 48
5
Answer the question.
Forty-eight litres of petrol could be purchased
for $50.88.
reMeMber
1. To divide a decimal by a whole number, set the question out as for division of whole
numbers and divide as for whole numbers.
2. The decimal point in the answer must be exactly in line with the decimal point in the
question.
3. When there is a remainder, add zeros to the end of the decimal and keep dividing until
there is no remainder.
4. When dividing a number by a multiple of 10, factorise the multiple to give a power of
10 and its other factor. Divide by the other factor first, and then by the power of 10.
5. To divide a decimal by a decimal, change the second decimal (the divisor) to a whole
number. This can be done by rewriting the question as a fraction, then multiplying both
numerator and denominator by whichever power of 10 makes the denominator a whole
number.
exerCise
6F
inDiViDuAl
pAThWAys
eBook plus
Activity 6-F-1
Dividing decimals
doc-1786
Dividing decimals (including by multiples of 10)
FluenCy
1 We24 Calculate:
a 3.6 ó 6
e 8.05 ó 5
i 17.847 ó 9
m 20.5782 ó 3
q 24.541 ó 11
b
f
j
n
r
21.7 ó 7
14.13 ó 3
8.029 ó 7
126.4704 ó 4
17.108 ó 14
c
g
k
o
s
17.4 ó 6
9.68 ó 4
32.5608 ó 8
37.56 ó 12
77.052 ó 12
d
h
l
p
t
4.86 ó 9
1.576 ó 2
41.8645 ó 5
46.80 ó 15
121.3421 ó 11
2 We25 Calculate the following. In each case, add zeros and keep dividing until there is no
remainder.
a 3.7 ó 2
210
b 9.5 ó 2
Maths Quest 7 for the Australian Curriculum
c 7.3 ó 5
d 9.8 ó 4
e 7.5 ó 6
f
55.6 ó 8