Answer:
[tex]\displaystyle \frac{265}{99}[/tex]
Step-by-step explanation:
Hi there!
Let [tex]x[/tex] be equal to the fraction form of the decimal.
[tex]x=2.\overline{67}[/tex]
Multiply both sides by 100:
[tex]100x=267.\overline{67}[/tex]
The reason we multiply both sides by 100 is that 2.6767... has two repeating decimals, 6 and 7, and 100 has two zeros.
Now, we have these two equations:
[tex]100x=267.\overline{67}[/tex]
[tex]x=2.\overline{67}[/tex]
Subtract [tex]x=2.\overline{67}[/tex] from [tex]100x=267.\overline{67}[/tex]:
[tex]100x=267.\overline{67}\\- x=2.\overline{67}\\\rule{70}{0.5}\\99x=265[/tex]
Isolate [tex]x[/tex] by dividing both sides by 99:
[tex]\displaystyle x=\frac{265}{99}[/tex]
I hope this helps!
