Page 23 - Mathematics

Converting fractions into repeating decimals

A fraction can be converted into a decimal by performing a long division. In this
process, some fractions will be equivalent to either terminating or non-terminating
decimals. If the resulting decimal is a non-terminating with recurring decimals,

the repeating digits are indicated by the repeating decimal’s notation. Tanzania Institute of Education

Example 2.7

Convert the following fractions into decimals.
1 2 5 17 387
(a) (b) (c) (d)
3 3 33 909

Solution
(a) Divide 1 by 3 using long division as (b) Divide 2 by 3 using long
follows and check your answer by a division as follows and
calculator. check your answer by a

0.3333... calculator.
31 0.6666...

− 0 32
10 − 0

− 9 20
10 − 18

− 9 20
− 18
10
− 9 20
10 − 18

− 9 20
1 − 18
 2
Mathematics Form One
1 

Therefore, = 0.3. 2

3 Therefore, = 0.6.
3

17

Mathematics form 1.indd 17 25/10/2024 09:51:05
25/10/2024 09:51:05
Mathematics form 1.indd 17