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 .
