Question

Rewrite 0.ababababab.... as a repeating fraction

Answer 1

It tells me that I got it wrong, but I will show my work here

Answer 2

try (10a+b)/99

Answer 3

\[\Large \color{red}{x}=0.ababab...\]
\[\Large \color{blue}{100x}=ab.ababab...\]



\[\Large \color{blue}{100x}=ab.ababab...\]
-
\[\Large \color{red}{x}=00.ababab...\]

\[\Large \color{green}{99x}=ab\]

\[\Huge x=\frac{ ab }{ 99 }\]

Answer 4

You're rihgt, just notice that ab is not a*b
"ab" is just the positional notation in decimal number system :

\[x = \dfrac{(ab)_{10}}{99} = \dfrac{10a+b}{99}\]

Answer 5

I don't understand

Answer 6

Oh, since a is in the 10s place, its actually 10a and b is in the ones place?

Answer 7

for example
\[0.131313...=\frac{13}{99}\]

Answer 8

I understand now.