# Decimal to fraction ?

##### 2 Answers

#### Explanation:

In general, when you have a number of the form

where

The reason this works is because if you multiply that repeating decimal by

Therefore,

It's also simple to find

#### Explanation:

#0. color(red)(3267)32673267....=0. bar(3267)#

#"the bar represents the digits being repeated"#

#"these form the terms of a "color(blue)"geometric sequence"#

#3267/10000,3267/100000000,...#

#"with "a=3267/10000#

#"and "r=a_2/a_1#

#rArrr=cancel(3267)/(10000cancel(0000))xx(1cancel(0000))/cancel(3267)=1/10000#

#â€¢color(white)(x)S_oo=a/(1-r)#

#rArrS_oo=(3267/10000)/(1-1/10000)#

#=(3267/10000)/(9999/10000)#

#=3267/9999=33/101#