Question

What is 2.31 repeating as a simplified fraction

Answer 1

Answer:

$2\frac{31}{99}$

Step-by-step explanation:

I am assuming that '.31' is the repeating pattern.

Setting up equation one:

$X=2.31313131....$

Setting up equation two:

There are two digits in the repeating group. I multiplied the first equation my 100 to get:

$100x=231.31...$

Subtract equation one from equation two:

'100x-231.3131..' - 'x = 2.313131... ' = '99x = 229'

Solve for X:

$99x=299\\\\99x/99=229/99\\\\\boxed{x=229/99}$

$\frac{229}{99}=2\frac{31}{99}$