.15 (5 repeating) as a fraction.

Question

Prior to this I got the answer 3/20, but when I divide I get .15 no fives repeating?

Answer 1

0.15 = 0.1555555,,,,,

0.1 + 0.05555555............. <--- splits the repeating part from the part that does not

0.1 + (1/10)*0.5 <--- moves the decimal in front of the 5 making that part 10 times larger than

it should be; so it multiplies by (1/10) to compensate

0.1 + (1/10)(5/9) <---- 1 repeating digit is changed to fraction by dividing by 9 rather than 10

(1/10) + (1/10)(5/9) <---- 0.1 = 1/10

(1/10) [ 1 + 5/9] <---- factors out 1/10

(1/10) [ 9/9 + 5/9] <---- common denominator

(1/10)[ 14/9] <---- adds the fractions

14/90 <---- multiplies the fractions