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

2 Answers

#a/b=229/900#

Explanation:

Let #a/b=0.25444444444444" "#first equation

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

#100a/b=25.444444444444" "#second equation

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

#1000a/b=254.44444444444" "#third equation

Subtract second from the third

#1000a/b-100a/b=254.44444444444-25.444444444444#

#900a/b=229#

#a/b=229/900#

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

Jun 1, 2016

#0.254444.... = (254-25)/900 = 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;

#"the digits which recur"/"a 9 for each digit"#

eg 0.777777...... = #7/9#

0.454545..... = #45/99 rArr "this can be simplified to" 5/11"#

5.714714714.... = #5 714/999 rArr 238/333#

#"2."# If only some digits recur:

#"all the digits - the non-recurring digits"/"a 9 for each recurring digit and 0 for each non-recurring digit"#

eg 0.3544444..... = #(354-35)/900 = 319/900#

eg. 0.4565656... = #(456-4)/990 = 452/990= 226/495#

eg 4.62151515... = #4 6215-62/9900 = 4 6153/9900 = 4 2051/3300#

0.254444.... = #(254-25)/900 = 229/900#

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