Question

2.6767.......

How do I write 2.67 w/ repeating 67 as a simplified fraction,...

Please show work (or provide explination)

Answer 1

`\displaystyle (265)/(99)`

Explanation:

Hi there!

Let
`x` be equal to the fraction form of the decimal.

`x=2.\overline{67}`

Multiply both sides by 100:

`100x=267.\overline{67}`

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:

`100x=267.\overline{67}`

`x=2.\overline{67}`

Subtract
`x=2.\overline{67}` from
`100x=267.\overline{67}`:

`100x=267.\overline{67}\\- x=2.\overline{67}\\\rule{70}{0.5}\\99x=265`

Isolate
`x` by dividing both sides by 99:

`\displaystyle x=(265)/(99)`

I hope this helps!