Question

How do you convert \[\dfrac{8}{15}\] to a decimal?

Answer 1

Hint: To convert \[\dfrac{8}{15}\] to a decimal, we need 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:
\[\dfrac{8}{15}\]
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 8 and denominator is 15 so dividing 8 by 15 we get,
\[15\overset{0.533}{\overline{\left){80}\right.}}\]
      \[\dfrac{75}{50}\]
      \[\dfrac{45}{50}\]
      \[\dfrac{45}{50}\]
In the above division, 3 are of repeating nature after the first term 5. Hence, the decimal representation of \[\dfrac{8}{15}\] is as follows:
0.5333333
Hence, from the above, we have converted the given fraction \[\dfrac{8}{15}\] into decimal and the decimal representation is equal to 0.5333.

Note: You can check whether the decimal representation is correct or not in the following way:
From the above, we got:
\[\dfrac{8}{15}=0.5333\]
Now, multiplying 15 on the both sides we get,
\[\dfrac{8}{15}\times 15=0.53333\times 15\]
\[\Rightarrow 8=7.9995\]
Now, if we round off the R.H.S of the above equation we will get 8 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 8 by 0.53333 and see whether the answer is nearly equal to 15 or not.
\[\dfrac{8}{0.5333}=15\]