Chapter 3
Decimals
3.1 Introduction
The decimal system of numbers is based on the digits
0 to 9.
There are a number of everyday occurrences in which we
use decimal numbers. For example, a radio is, say, tuned
to 107.5 MHz FM; 107.5 is an example of a decimal
number.
In a shop, a pair of trainers cost, say, £57.95; 57.95 is
another example of a decimal number. 57.95 is a decimal
fraction, where a decimal point separates the integer, i.e.
57, from the fractional part, i.e. 0.95
57.95 actually means (5 × 10) + (7 × 1)
+
9 ×
1
10
+
5 ×
1
100
3.2 Converting decimals to fractions
and vice-versa
Converting decimals to fractions and vice-versa is
demonstrated below with worked examples.
Problem 1. Convert 0.375 to a proper fraction in
its simplest form
(i) 0.375 may be written as
0.375 × 1000
1000
i.e.
0.375 =
375
1000
(ii) Dividing both numerator and denominator by 5
gives
375
1000
=
75
200
(iii) Dividing both numerator and denominator by 5
again gives
75
200
=
15
40
(iv) Dividing both numerator and denominator by 5
again gives
15
40
=
3
8
Since both 3 and 8 are only divisible by 1, we cannot
‘cancel’ any further, so
3
8
is the ‘simplest form’ of the
fraction.
Hence, the decimal fraction 0.375 =
3
8
as a proper
fraction.
Problem 2. Convert 3.4375 to a mixed number
(i) 0.4375 may be written as
0.4375 × 10000
10000
i.e.
0.4375 =
4375
10000
(ii) Dividing both numerator and denominator by 25
gives
4375
10000
=
175
400
(iii) Dividing both numerator and denominator by 5
gives
175
400
=
35
80
(iv) Dividing both numerator and denominator by 5
again gives
35
80
=
7
16
Since both 5 and 16 are only divisible by 1, we
cannot ‘cancel’ any further, so
7
16
is the ‘lowest
form’ of the fraction.
(v) Hence, 0.4375 =
7
16
Thus, the decimal fraction 3.4375 = 3
7
16
as a mixed
number.
DOI: 10.1016/B978-1-85617-697-2.00003-X