Question

How do you write \[\dfrac{27}{99}\] as a decimal?

Answer 1

Hint: To convert \[\dfrac{27}{99}\] to a decimal, we need to first look for common terms. Here, we find that 9 are divisible by both numerator and denominator. Simplify the fraction by cancelling the common term 9. We get \[\dfrac{3}{11}\]. Now, we have to divide the numerator of a fraction by the denominator of a fraction and then see what kind of decimal expression we are getting. In fraction, the numerator is the number which is written above the fraction and denominator is the number which is written below the fraction.

Complete step-by-step solution:
The number which is given in the above problem of which we have to find the decimal expression is as follows:
\[\dfrac{27}{99}\]
First, we have to look for the common terms in the numerator and denominator.
We find that \[\dfrac{27}{99}=\dfrac{9\times 3}{9\times 11}\].
Here, 9 is common in both the numerator and denominator. Cancelling out the common term 9, we get
\[\dfrac{27}{99}=\dfrac{3}{11}\]
Now, we have to find the decimal of \[\dfrac{3}{11}\].
As you can see that the above number is in the form of a fraction so to find the decimal expression of the above number we have to divide the numerator of the fraction by the denominator. The numerator of the above number is 3 and denominator is 11 so dividing 3 by 11 we get,
\[11\overset{0.2727}{\overline{\left){30}\right.}}\]
      \[\dfrac{22}{80}\]
      \[\dfrac{77}{30}\]
      \[\dfrac{22}{80}\]
      \[\dfrac{77}{30}\]
In the above division, 2 and 7 are repeating alternatively. Hence, the decimal representation of \[\dfrac{3}{11}\] is as follows:
0.2727
Hence, from the above, we have converted the given fraction \[\dfrac{27}{99}\] into decimal and the decimal representation is equal to 0.2727.

Note: You can check whether the decimal representation is correct or not in the following way:
From the above, we got:
\[\dfrac{27}{99}=0.2727\]
Now, multiplying by 99 on the both sides we get,
\[\dfrac{27}{99}\times 99=0.2727\times 99\]
\[\Rightarrow 27=26.9973\]
Now, if we round off the R.H.S of the above equation we will get 27 which means that L.H.S is equal to R.H.S so the decimal representation that we have written in the solution is correct.
In this way, you can divide 27 by 0.2727 and see whether the answer is nearly equal to 99 or not.
\[\dfrac{27}{0.2727}=99\]