# How can you convert a decimal to fraction?

##### 1 Answer

See explanation...

#### Explanation:

If it is a terminating decimal, then multiply it by a power of

For example:

#0.16 = 16/100 = (color(red)(cancel(color(black)(4)))*4)/(color(red)(cancel(color(black)(4)))*25) = 4/25#

If it is a repeating decimal, then multiply by a power of

For example:

#0.2345345345... = 0.2bar(345)#

Multiply by

#(10000-10)0.2bar(345) = 2345.bar(345) - 2.bar(345) = 2343#

So, dividing by

#0.2bar(345) = 2343/(10000-10) = 2343/9990 = (color(red)(cancel(color(black)(3)))*781)/(color(red)(cancel(color(black)(3)))*3330) = 781/3330#