How do you convert 0.03 (3 repeating) to a fraction?

1 Answer
Jul 5, 2016

#0.0bar(3) = 1/30#

Explanation:

As a general method for converting repeating decimals to fractions, suppose that the repeating portion is #n# digits long. Then let #x# represent the initial value, and using the fact that #10^nx-x# has finitely many digits, solve for #x# to find the fraction.

In this case, #3# is the repeating portion, which has #1# digit. Thus, we will let #x=0.0bar(3)# (the bar denotes repeating digits) and multiply by #10^1#.

#x = 0.0bar(3)#

#=>10x = 0.bar(3)#

#=>10x-x = 0.bar(3)-0.0bar(3)#

#=> 9x = 0.3#

#=> x = 0.3/9 = 3/90 = 1/30#