Converting Fractions to Decimals (and vice versa) – Study Guide 3 Page 1
Converting Fractions to Decimals (and vice versa)
It is easy to change a fraction to a decimal and a decimal to a fraction. You just need to
understand that fractions and decimals are just numbers and/or parts of numbers expressed
in different ways.
DECIMAL REVIEW
The Decimal System is another way of expressing a part of a whole number. A decimal is simply
a fraction with a denominator of 10, 100, 1 000 or 10 000 etc. The number of decimal places
refers to how many zeros will be in the denominator.
The first decimal place refers to tenths
3
2.3 210
The second decimal place refers to hundredths
31
2.31 2100
The third decimal place refers to thousandths
319
2.319 21000
Similarly, six decimal places would be a fraction with a denominator of 1 000 000
(millionths). The most common usage of decimals is in our monetary system where 100
cents (2 decimal places) make up one dollar. For example, $2.41 is really two dollars and
forty-one hundredths
41
()
100
of a dollar.
Changing Decimals into Fractions
Example 1: Change 7.95 into a fraction
To change this decimal into a fraction, write down the whole number first:
7 is a whole number
Now look at the numbers after the decimal point (.95). This is a fraction of a whole number:
95 ‘somethingths’.
To work out what those ‘somethingths’ are, look at how many decimal places are being used:
The number 9 is in the tenths column, and the 5 is in the hundredths column.
This means that we have 95 hundredths or 𝟗𝟓
𝟏𝟎𝟎
So, 7.95 = 7 95
100 (you can simplify this to make 95
100 =19
20 )
