Question

How do you convert $\dfrac{8}{{15}}$ as a decimal?

Answer 1

Hint: Here, we are required to convert the given fraction as a decimal. Thus, as we can observe that we cannot simplify this fraction further and there is no way that we convert the denominator as a multiple of 10. Thus, we have no other choice than dividing the numerator by the denominator. Thus, by dividing this and solving this further, we will be able to convert the given fraction as a decimal.

Complete step-by-step answer:
In order to convert the given fraction into decimal, we will divide the numerator by denominator as:
          \[0.53\]
\[15)\overline {8\,\,\,\,\,\,} \]
       \[
  \underline {75\,\,\,\,\,\,\,\,} \\
 0\;50
 \]
         \[
   45 \\
    \overline {\,\,5\,\, } \\
 \]
Since, when 8 is divided by 15, after the digit 5 present after the decimal point, the number 3 keeps on repeating, thus, instead of writing 3 so many times, we can add a bar on 3 to represent its repetition.
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are periodic i.e. repeating its values at regular intervals and the infinitely repeated portion is not zero.

Therefore, $\dfrac{8}{{15}}$ can be written as $0.5\overline 3 $ as a decimal.
Thus, this is the required answer.

Note:
An alternate way of solving this fraction and converting this to decimal is:
Given fraction is: $\dfrac{8}{{15}}$
Multiply the numerator and the denominator by 2, we get,
$\dfrac{{8 \times 2}}{{15 \times 2}} = \dfrac{{16}}{{30}}$
Now, multiplying numerator and denominator by 3333333,
$ \Rightarrow \dfrac{8}{{15}} = \dfrac{{16}}{{30}} = \dfrac{{16 \times 3333333}}{{30 \times 3333333}} = \dfrac{{53333328}}{{99999990}}$
Now, by approximation, we can write $99999990 = 100000000$
Hence, we get,
$ \Rightarrow \dfrac{8}{{15}} = \dfrac{{53333328}}{{100000000}} \cong 0.53333328$
But since, we have used approximation and we know that $99999990 < 100000000$
Therefore,
$ \Rightarrow \dfrac{8}{{15}} > 0.53333328$
Hence, we can write this as:
$\dfrac{8}{{15}} = 0.5333333...$
Therefore, $\dfrac{8}{{15}}$ can be written as $0.5\overline 3 $ as a decimal.
Thus, this is the required answer.