Question

How do you convert \[\dfrac{3}{{11}}\] to a decimal?

Answer 1

Hint: Here we will first rewrite the given fraction such that the denominator of the fraction becomes a multiple of 10. Then we will apply a simple division operation to get the decimal form of the given fraction.

Complete step by step solution:
The fraction is \[\dfrac{3}{{11}}\].
First, we will rewrite the given fraction so that the denominator of the given fraction becomes in terms of the ten or hundred or thousand or near it.
Therefore, we will multiply numerator and denominator by 9 to get the 99 in the denominator which is almost equal to 100. Therefore, we get
\[\dfrac{3}{{11}} = \dfrac{{3 \times 9}}{{11 \times 9}}\]
Now after solving the above equation, we get
\[ \Rightarrow \dfrac{3}{{11}} = \dfrac{{27}}{{99}}\]
We can see that the denominator is one less than 100. So, we can write the equation as
\[ \Rightarrow \dfrac{3}{{11}} = \dfrac{{27}}{{100}}\]
Now by simply division operation we will get the decimal form of the given fraction. Therefore, we get
\[ \Rightarrow \dfrac{3}{{11}} = 0.27\]

Hence, the decimal form of the fraction \[\dfrac{3}{{11}}\] is \[0.27\].

Note:
Any number can be represented in decimal form. We do not need to write whole numbers in decimal form because it is already implied. For example, 34.00 can simply be written as 34. The fraction given in our question is of a proper fraction. We should know that there are three types of fractions i.e. proper fractions, improper fractions, and mixed fractions.