Question

How do you write \[5\dfrac{9}{{10}}\] as a decimal?

Answer 1

Hint: We know that fraction is a part of whole. Here we are given with a mixed fraction. We have to convert this into an improper fraction. For that we will multiply the denominator with the whole number and then add it to the numerator this is the process. And when we write this this denominator is the same.
Mixed fraction to improper fraction
\[ \Rightarrow \dfrac{{{\text{denominator} \times \text{whole number + numerator}}}}{{{\text{denominator}}}}\]
Once we convert it into improper we will directly divide the numerator by the denominator to get the decimal value answer.

Complete step-by-step answer:
Given that is a mixed fraction \[5\dfrac{9}{{10}}\] .
While converting into the improper fraction we will use the formula mentioned above.
Mixed fraction to improper fraction
\[ \Rightarrow \dfrac{{{\text{denominator} \times \text{whole number + numerator}}}}{{{\text{denominator}}}}\]
 \[5\dfrac{9}{{10}} \Rightarrow \dfrac{{{\text{10}} \times {\text{5 + 9}}}}{{10}}\]
On solving this we get,
 \[5\dfrac{9}{{10}} \Rightarrow \dfrac{{{\text{50 + 9}}}}{{10}}\]
On adding the numbers in numerator
 \[5\dfrac{9}{{10}} \Rightarrow \dfrac{{59}}{{10}}\]
Now we have the mixed fraction converted into improper form. Now to find the decimal form, we will divide the numerator by the denominator. Rather here the denominator is 10. So dividing a number by 10 means shifting the decimal one place left. So that is
 \[5\dfrac{9}{{10}} = 5.9\]
This is our final answer.
So, the correct answer is “5.9”.

Note: Note that denominator doesn’t change. Also we can cross verify that the answer so obtained has a numerator greater than denominator so that is an improper fraction. Also remember mixed fractions are never converted into proper fractions because the denominator is always less than the numerator. To find decimals we also can divide the numbers but this method used is easier.