How do you convert 5.8 to a simplified fraction?

This number can be represented in simple fraction form as
^{
29
}
⁄
_{
5
}
.

Here is how you can obtain this answer step-by-step.

## Convert 5.8 To Fraction Form

The easiest way I know of converting a decimal number into a fraction is as follows.

Step 1: Count how many numbers are
*
after
*
the decimal place. With the number 5.8, there is 1 number
*
after
*
the decimal place.

5.\fcolorbox{red}{yellow}{8}

Step 2: Raise the number in step 1 to the power of 10:

10^{\fcolorbox{red}{yellow}{1}} = 10

Step 3: Create a fraction with your original number
*
without
*
the decimal point in the numerator and the number in step 2 as the denominator:

\frac{58}{10}

Step 4: Finding the highest common factor between both numbers and reduce. The highest common factor between 58 and 10 is the number 2:

\frac{58 \div 2}{10 \div 2} = \frac{29}{5}

And you should have your answer!

5.8 = \frac{58}{10}

## Convert 5.8 To Simple Fraction: Checking Your Answer

How can you check your answer to confirm it’s right?

With the fraction portion of the result wrap it into short division. Remember, when creating a short division problem from a fraction the
**
denominator
**
is the
**
divisor
**
and the
**
numerator
**
is the
**
dividend
**
.

Here’s how the fraction looks when changed to division:

\fcolorbox{red}{yellow}{5} \ \overline{\smash{\Large{)}} \ \fcolorbox{red}{yellow}{29} }

Step through each individual number in the dividend.

How many times does 5 go into 2? It doesn’t, therefore, we carry the remainder of 2 over to the next number:

\fcolorbox{red}{yellow}{5} \ \overline{\smash{\Large{)}} \ \fcolorbox{red}{yellow}{2} \ 9 \ } \\ \ \\ 5 \ \overline{\smash{\Large{)}} \ 2^{\ \fcolorbox{red}{yellow}{2}} \ 9 \ }

How many times does 5 go into 28?

It goes 5 times remainder 4.

\begin{aligned} \ \ \ \ \ \ \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ & \\ 5 \ \overline{\smash{\Large{)}} \ 2^{ \ 2 } \ 9\fcolorbox{red}{yellow}{.}^{ \ \fcolorbox{red}{yellow}{4} } \ \fcolorbox{red}{yellow}{0} } & \end{aligned}

As you have reached the end of your number 29 you need to add a decimal place followed by a zero. The continue on:

Ignoring the decimal point, how many times does 5 go into 40? It goes exactly eight times:

\begin{aligned} \ \ \ \ \ \ \ 5 \fcolorbox{red}{yellow}{.} \fcolorbox{red}{yellow}{8} & \\ 5 \ \overline{\smash{\large{)}} \ 2^{ \ 2 } \ 9.^{ \ 4 } \ 0} & \end{aligned}

As you can see the answer from performing the division of the fraction produces the same result as the original decimal number.

This confirms the fraction
^{
29
}
⁄
_{
5
}
is correct.

## Summary

How do you change the decimal number 5.8 to a fraction? Start by placing the decimal portion of the number as the numerator and then count how many numbers are in the numerator and write down a zero for each number then put a 1 in front of the zeroes.

See if there is a common factor between both numbers, and if there is, reduce both the numerator and the denominator by the highest common factor.

Therefore, 5.8 will produce the simple fraction of
^{
29
}
⁄
_{
5
}
.