Question

How do you convert $0.8$ ($8$repeating) to a fraction?

Answer 1

Hint: $0.8$ is a repeating decimal number and you want to convert it to a fraction or mixed number. When you say $0.8$ repeating, you mean that the $1$ is repeating. Here is the question formulated in mathematical terms with the vinculum line above the decimal number that is repeating.

Formula used:
The formula to convert any repeating decimal number to a fraction is as follows:
$\dfrac{{(DN \times F) - NRP}}{D}$
Here, DN is Decimal Number. F is $10$ if one repeating number, $100$ if two repeating numbers, $1000$ if three repeating numbers, etc. NRP is Non-repeating part of the decimal number. D is $9$ if one repeating number, $99$ if two repeating numbers, $999$ if three repeating numbers, etc.

Complete step-by-step answer:
The formula to convert any repeating decimal number to a fraction is as follows:
$\dfrac{{(DN \times F) - NRP}}{D}$
Below shows you how to get the answer to $0.8$ repeating as a fraction using our formula.
$ = \dfrac{{(0.8 \times 10) - 0}}{9} $
$ = \dfrac{8}{9} $
Below is the answer in the simplest form possible:

$0.8$ repeating as a fraction
$ = \dfrac{8}{9}$

Note: There are many methods for solving this type of questions but I think this is the best and easy way to solve this question. You just have to remember the formula and you can solve any repeating decimal number to a fraction.