How do you convert 5.8 to a simplified fraction?
This number can be represented in simple fraction form as $\frac{29}{5}$.
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:
$$ 5.\boxed{8} $$
Step 2
Raise the number 10 to the power of how many digits are after the decimal:
$$ 10^1 = 10 $$
Step 3
Create a fraction with your original number without the decimal point in the numerator and 10 as the denominator:
$$ \frac{58}{10} $$
Step 4
Reduce the fraction by dividing both numerator and denominator by their highest common factor. The HCF of 58 and 10 is 2:
$$ \frac{58 \div 2}{10 \div 2} = \frac{29}{5} $$
So the simplified fraction form of 5.8 is:
$$ 5.8 = \frac{29}{5} $$
Check Your Answer Using Division
To confirm the result is correct, convert $\frac{29}{5}$ back into a decimal using short division.
That means dividing the numerator 29 by the denominator 5:
$$ 5 , \overline{\smash{\big)} , 29} $$
How many times does 5 go into 2? It doesn’t. So we carry the 2 over to make 29.
How many times does 5 go into 29? It goes 5 times (5×5 = 25), remainder 4.
Now, bring down a 0 to continue division into decimals:
$$ 5 , \overline{\smash{\big)} , 29.0} = 5.8 $$
Thus, the decimal result is the same as the original number, confirming the conversion is correct.
Summary
To change the decimal number 5.8 into a fraction:
- Write it as $\frac{58}{10}$
- Simplify by dividing top and bottom by their greatest common factor (2)
- Final result: $\frac{29}{5}$
This confirms that the decimal 5.8 is equal to the simplified fraction $\frac{29}{5}$.