\(Express 0.5\overline{10} as a common fraction.\)

Guest Aug 31, 2020

edited by
Guest
Aug 31, 2020

edited by Guest Aug 31, 2020

edited by Guest Aug 31, 2020

edited by Guest Aug 31, 2020

edited by Guest Aug 31, 2020

#2**+1 **

@OP: I'm not sure why you posted this as off-topic

@guest that answered: I'm not sure if you can see the LaTeX, but \overline{} means "repeating decimal", not fraction. (the command for fraction is \frac{}{} or \dfrac{}{} depending on what size you want it to be)

**The answer begins here:**

Because my LaTeX is not working, I will do my best to write the fractions and repeating decimals.

We want to convert this to a fraction:

––

0.510, which is 0.51010101010101010101010.....

To begin, let's call this fraction "x". Based on what we know:

1000x = 510.10101010...

10x = 5.101010101010...

Subtract one from the other:

990x = 505

Divide by 990:

x = 505/990 = **101/198**

**:)**

ilorty Aug 31, 2020