Question

How do you convert $${\displaystyle \frac{8}{50}}$$ to a decimal?

Answer 1

Hint: This is the given number in fraction form. It is having a numerator and denominator. As we need to convert it in decimal we will perform the division as 8 divided by 50. We will write the denominator in terms of multiple of 10 so that we can divide 8 by 5 and then the answer is divided by 10 such that the decimal point will be shifted just one place to the left.

Complete step by step solution:
Given that $${\displaystyle \frac{8}{50}}$$.This is a fraction. Now we can write the denominator as
$${\displaystyle \frac{8}{5\times 10}}$$
Separating two fractions we get,
$${\displaystyle \frac{8}{5}}\times {\displaystyle \frac{1}{10}}$$
On dividing 8 by 5 we get,
$$5\stackrel{{\displaystyle 1}}{)\phantom{1\begin{array}{c}8\\ -5\\ \overline{3}\end{array}}\overline{\phantom{1}\begin{array}{c}8\\ -5\\ \overline{3}\end{array}}}$$
Now for 3 to be remainder we will take a decimal point in the quotient such that it adds a zero to the remainder.
$$5\stackrel{{\displaystyle 1.}}{)\phantom{1\begin{array}{c}8\\ -5\\ \overline{3}\overline{0}\end{array}}\overline{\phantom{1}\begin{array}{c}8\\ -5\\ \overline{3}\overline{0}\end{array}}}$$
Now we will divide 30 by 5 such that
$$5\stackrel{{\displaystyle 1.6}}{)\phantom{1\begin{array}{c}8\\ -5\\ \overline{3}\overline{0}\\ -30\\ \overline{0}\overline{0}\end{array}}\overline{\phantom{1}\begin{array}{c}8\\ -5\\ \overline{3}\overline{0}\\ -30\\ \overline{0}\overline{0}\end{array}}}$$
This completes the division as the remainder is zero. Now we can write the fraction as,
$$1.6\times {\displaystyle \frac{1}{10}}$$
On dividing with 10 the decimal shifts,
$$0.16$$

So we can write $${\displaystyle \frac{8}{50}}=0.16$$.

Note: Here note that we are given with a fraction in the form of numerator and denominator. The decimal form is a number with a decimal point. If the numerator is smaller than the denominator then we call it a proper fraction. Note that we cannot divide 8 by 50 so we converted 50 as a product in the form of 10. And then the fraction so formed can be easily divided.