# How do you convert 0.254 (4 repeating) as a fraction?

$\frac{a}{b} = \frac{229}{900}$

#### Explanation:

Let $\frac{a}{b} = 0.25444444444444 \text{ }$first equation

Multiply both sides of the first equation by 100 and the result is

$100 \frac{a}{b} = 25.444444444444 \text{ }$second equation

Multiply both sides of the first equation by 1000 and the result is

$1000 \frac{a}{b} = 254.44444444444 \text{ }$third equation

Subtract second from the third

$1000 \frac{a}{b} - 100 \frac{a}{b} = 254.44444444444 - 25.444444444444$

$900 \frac{a}{b} = 229$

$\frac{a}{b} = \frac{229}{900}$

God bless....I hope the explanation is useful

Jun 1, 2016

$0.254444 \ldots . = \frac{254 - 25}{900} = \frac{229}{900}$

#### Explanation:

There are easy rules to use for converting recurring decimals to fractions:
There are 2 types of recurring decimals - those where ALL the digits recur and those where SOME of the digits recur.

1. If ALL the digits recur, the fraction is formed from;

$\text{the digits which recur"/"a 9 for each digit}$

eg 0.777777...... = $\frac{7}{9}$

0.454545..... = $\frac{45}{99} \Rightarrow \text{this can be simplified to" 5/11}$

5.714714714.... = $5 \frac{714}{999} \Rightarrow \frac{238}{333}$

$\text{2.}$ If only some digits recur:

$\text{all the digits - the non-recurring digits"/"a 9 for each recurring digit and 0 for each non-recurring digit}$

eg 0.3544444..... = $\frac{354 - 35}{900} = \frac{319}{900}$

eg. 0.4565656... = $\frac{456 - 4}{990} = \frac{452}{990} = \frac{226}{495}$

eg 4.62151515... = $4 6215 - \frac{62}{9900} = 4 \frac{6153}{9900} = 4 \frac{2051}{3300}$

0.254444.... = $\frac{254 - 25}{900} = \frac{229}{900}$

These rules are short cuts for algebraic methods, but it is often useful to be able to get to answer immediately.