Page 19 - Mathematics

Examples of terminating decimals are 0.5, 1.4, and 7.9 while non-repeating decimals
are 3.1415926..., 1.4142135…., and 2.2360679…

Converting repeating decimals into fractions
When working with problems involving repeating decimals, it is important to convert
them into simple fractions to maintain accuracy and avoid errors. A repeating Tanzania Institute of Education
decimal can be converted into fraction using the following steps:
1. Choose any variable to represent the required fraction.
2. Multiply both sides of the equation by a multiple of 10 depending on the


number of repeating decimals. For example, 0.8 and 0.213 have only one

repeating digit which means they are multiplied by 10. Decimal numbers


0.11and 1.214 have two repeating digits, thus they are multiplied by 100,
 
and 0.835 will be multiplied by 1,000 since it has 3 repeating digits.

3. Subtract the equation in step 1 from the equation in step 2.
4. From the equation obtained in step 3, solve for the chosen variable and
simplify where necessary.

Example 2.5

Convert each of the following decimals into fractions.

 


(a) 0.3 (b) 0.83 (c) 0.835 (d) 0.83
Solution

(a) Let x = 0.3 (i)
Multiply by 10 both sides of equation (i) to obtain,

10x = 3.3 (ii)
Subtract equation (i) from equation (ii) as follows:


10xx−= 3.3 0.3− 
Thus, 9x = 3
1
x =
3 1

Therefore, 0.3into fraction is .
3

(b) 0.83
Let .0.83x =  (i) Mathematics Form One
Multiply by 100 both sides of equation (i) to obtain

100x = 83.83 (ii)

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Mathematics form 1.indd 13