Question

How do you change ${\displaystyle \frac{5}{8}}$ into a decimal?

Answer 1

Hint: In order to solve this question we need to use the concept of decimal numbers carefully, in which the numbers are written with the help of a dot like so ‘ . ’. Since it is a fraction and we need to convert a fraction in a decimal form, we will use here the method of division to get the answer.

Complete step by step solution:
A decimal form is a representation of any number, mostly non-integers and integers, into a number which has a denominator as 1. Moreover, the number is itself denoted with the help of a point. The numbers like, 1.23, 5.2 and so on are called decimal numbers. We use this form of numbers so that we do not write these in fractional form.
Now, simply consider the given number ${\displaystyle \frac{5}{8}}$. Clearly, it is in fractional form. So to convert it into a decimal form, we will divide them as below. Since, the numerator 5 is smaller than the denominator 8 therefore, we will divide 50 by 8 instead of 5 and take one decimal as shown below.
$8\stackrel{0.625}{\overline{)\begin{array}{rl}& +50\\ & \underset{―}{\pm 48}\\ & +20\\ & \underset{―}{\pm 16}\\ & +40\\ & \underset{―}{\pm 40}\\ & 0\end{array}}}$
Thus, the fraction ${\displaystyle \frac{5}{8}}$ is written as 0.625.

Note: This we all know that if there is an additional sign then we add two numbers and subtract if there is a sign of -. But here, we have got + 50 and + (- 48). In this case, + (- 48) will be written as – 48. Thus, we will solve it as + 50 – 48 = +2. If there would have been an irrational number then, we cannot convert it into decimal. Only rational numbers get a chance of being written as decimals. To solve such questions one should know the concepts of rational, integers, non-integers and decimal numbers clearly. Moreover, division is required here otherwise; we may get a wrong answer.