What is the fractional equivalent of the repeating decimal n=0.1515...?

1 Answer
Jan 26, 2018

#0.1515bar15-=15/99#

Explanation:

We need to devise some method to 'get rid of the repeating part then turn whats left into a fraction. We can use the fact that it repeating to our advantage.

Set #x=0.1515bar15" "...Equation(1)#

the #bar15# means that those two digits keep repeating for ever.

So

#100x=15.1515bar15" "...............Equation(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtract 1 of the equations from the other

#100x=15.1515bar15#
#ul(color(white)(100)x=color(white)(1)0.1515bar15 larr" Subtract"#
#color(white)(1)99x=15#

Divide both sides by 99

#x=15/99#