Question

Convert each repeating decimal to a simplified fraction. Show your work.

0.77--
2.3-
1.013--

Answer 1

Say x = 0.77--
Then 10x = 7.7--
Then 10x - x = 7 => 9x=7 => x=7/9

Say x = 2.3-
10x = 23.3-
10x-x = 9x = 21 => x = 21/9

last one is a bit tougher because it has alternating digits

Say x = 1.013--
100x = 101.313--
100x-x = 99x = 100.3 = x = 1003/990

I multiplied the final fraction with 10 to get integers.