Question

How do you convert $0.625$ into a percent and fraction?

Answer 1

Hint:
For converting the number in the fraction, start with equating the number with a variable ‘m’. Now multiplying the both sides of the equation with $1000$ . Now transpose the numbers to one side to form a fraction. Change it to the simplest form for getting the required answer. For changing it to the percentage, multiply the fraction with $100$ and solve it.

Complete Step by step Solution:
Here in this problem, we are given a number $0.625$ and we need to convert it into percent form and fraction.
Before starting with the solution we should understand a few concepts of fractions and percentages. A fraction describes a part of a whole. The number on the bottom of the fraction is called the denominator, and it denotes how many equal parts the whole is divided into. The number on the top of the fraction is called the numerator, and it denotes how many of the parts we are taking.
If the fraction is having a numerator smaller than the denominator, then it is known as the proper fraction. And if the fraction is having a numerator greater than the denominator, then it is known as the improper fraction.
Here in this case we have a number $0.625 < 1$ , which is less than $1$ , and thus can be converted to in its proper fraction form.
For changing it into a fraction, let’s equate this number with a variable ‘m’
$ \Rightarrow m = 0.625$
Now, we have three digits after the decimal. So multiply both sides with $1000$ and we have:
$ \Rightarrow m \times 1000 = 0.625 \times 1000 \Rightarrow 1000m = 625$
So we removed the decimal from the right side. For obtaining the fraction, we can transpose $1000$ from left side to right side, we get:
$ \Rightarrow 1000m = 625 \Rightarrow m = \dfrac{{625}}{{1000}}$
We got the fraction but it is not in the simplest form. For getting the simplest form, we can divide both numerator and denominator by the same number:
$ \Rightarrow m = \dfrac{{625}}{{1000}} \Rightarrow m = \dfrac{{\dfrac{{625}}{{25}}}}{{\dfrac{{1000}}{{25}}}} = \dfrac{{25}}{{40}}$
Again dividing both numerator and denominator by $5$ to get the simplest form
$ \Rightarrow m = \dfrac{{\dfrac{{25}}{5}}}{{\dfrac{{40}}{5}}} = \dfrac{5}{8}$
Thus, we get the fraction form of $0.625$ as $\dfrac{5}{8}$ .
A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount. For changing a fraction into a percentage we multiply it with $100$
For this case, we get:
$ \Rightarrow $ Percentage form of $0.625$ $ = \dfrac{5}{8} \times 100 = \dfrac{5}{2} \times 25 = \dfrac{{125}}{2} = 62.5\% $

Hence, we converted the number $0.625$ into $\dfrac{5}{8}$ and percent as $62.5\% $.

Note:
In this question, the use of fundamental concepts of fractions was a crucial part of the solution. Notice that we multiplied the number $0.625$ by a thousand because the motive was to remove the decimal point from the number. Multiplying a number with $10$ will shift the decimal one place to the left. Notice that the original number was $0.625$ and the percentage was $62.5\% $, which is the same as multiplying $0.625$ with hundred.