+0  
 
0
75
2
avatar

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

off-topic
 Aug 31, 2020
edited by Guest  Aug 31, 2020
edited by Guest  Aug 31, 2020
edited by Guest  Aug 31, 2020
 #1
avatar
0

0.5/10= 5/100 so 1/20

 Aug 31, 2020
 #2
avatar+1039 
+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

 

:)

 Aug 31, 2020

15 Online Users

avatar