Question

How do you change fractions to a decimal and a percent?

Answer 1

Hint: We are asked to write as to how do we go about converting a fraction to a decimal and a percent. A fraction consists of a numerator and a denominator. So, when you divide the numerator by the denominator using the arithmetic division, we will get a quotient which will have the fraction in decimal form. So, we have the decimal form. Now, we have to find the percent. For this, we will multiply the decimal form which we just found out by 100, so the decimal place will shift two places towards the right and what we get is the percent of the given fraction.

Complete step by step solution:
According to the given question, we are asked to write how to convert a given fraction into a decimal and a percent.
A fraction is ratio of a numerator and a denominator and it is represented as \[\dfrac{a}{b}\], where ‘a’ is the numerator and ‘b’ is the denominator.
We are asked to show first how to convert a fraction to a decimal.
A decimal number is a number having a decimal point in it. For example - \[3.14\], etc.
So, if we want to convert a fraction to a decimal form, we will have to divide the numerator by the denominator using the simple arithmetic division. On division, we will get a quotient and that quotient is the decimal form of the given fraction having decimal point in it as well.
For example – suppose, we have a fraction, \[\dfrac{3}{4}\] and we have to convert this fraction into decimal form, we will carry out the division operation. We have,
\[4\overset{0.75}{\overline{\left){\begin{align}
  & 3 \\
 & \underline{-0} \\
 & 30 \\
 & \underline{-28} \\
 & 20 \\
 & \underline{-20} \\
 & \_0\_ \\
 & \\
\end{align}}\right.}}\]
We get the quotient as \[0.75\] and it is the decimal form of the fraction \[\dfrac{3}{4}\].
That is, \[\dfrac{3}{4}=0.75\]
Now, we have to convert a fraction to a percent.
Per cent refers to a quantity for every hundred.
Earlier, we had converted fraction to decimal form. So, from a decimal form, we only have to multiply by 100 to get the percent of a given fraction.
For example - continuing the above example,
We had obtained the decimal equivalent as \[\dfrac{3}{4}=0.75\].
To get the percent, we will multiply by 100, we get,
\[0.75\times 100=75%\]
Therefore, \[\dfrac{3}{4}=75%\]

Note: The process of from a fraction to a decimal form and from a fraction to a percent is interlinked, that is, if we know the decimal equivalent of a fraction we can simply multiply it with 100 and get the percent and if the decimal form is not known, we need not find the decimal form first, we can do it directly as well,
\[\dfrac{3}{4}\times 100=3\times 25=75%\]