Question

Find an equivalent fraction for the decimal number. In your final answer, include all of your work.

Answer 1

Answer:

$\frac{901}{999}$

Step-by-step explanation:

we know that

A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.

In this problem we have

0.901 recurring

that means

0.901901901..

Let

$x=0.901901901..$

Multiply x by a power of  $10$, one that keeps the decimal part of the number the same:  

$1,000x=901.901901..$

Subtract $x$ from $\\1000x$

$1,000x-x=901.901901..-0.901901..=901$

The repeating decimals should cancel out

$\\999x=901$

solve for x

Divide by $999$ both sides

$990x/990=135/990$

$x=\frac{901}{999}$