Question

How do you convert 0.625 into a fraction and percent ?

Answer 1

Hint: For converting the number in the fraction, start with equating the number with a variable ‘x’. 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
Here 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 ‘x’.
$$\Rightarrow x=0.625$$
Now, we have three digits after the decimal. So multiply both sides with 1000 and we have:
$$\begin{array}{rl}& \Rightarrow x\times 1000=0.625\times 1000\\ & \Rightarrow 1000x=625\end{array}$$
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:
$$\Rightarrow x={\displaystyle \frac{625}{1000}}$$
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:
$$\Rightarrow x={\displaystyle \frac{625}{1000}}$$ = $${\displaystyle \frac{{\displaystyle \frac{625}{125}}}{{\displaystyle \frac{1000}{125}}}}={\displaystyle \frac{5}{8}}$$
Thus, we get the fraction form of 0.625 as $${\displaystyle \frac{5}{8}}$$ .
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
$$\Rightarrow {\displaystyle \frac{5}{8}}\times 100={\displaystyle \frac{125}{2}}=62.5\mathrm{\%}$$
Hence, we converted the number 0.625 into $${\displaystyle \frac{5}{8}}$$ and percent as $$62.5\mathrm{\%}$$.

Note: In this question, the use of fundamental concepts of fractions has 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.