Mathematics: Please help me with this equation

Please help me with this equation - id8797682, aliami0306oyaj0n

gilliancarter2202

19.07.2020

$\displaystyle \frac{265}{99}$

Step-by-step explanation:

Hi there!

Let 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 by dividing both sides by 99:

$\displaystyle x=\frac{265}{99}$

I hope this helps!

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