Converting Percentage to Fraction, Decimal, Ratio: The percentage is used to compare different values. Fractions, decimals, ratios, and percents are various alternative ways to express any number. Converting percent to fraction, decimals, ratio, and vice versa are the most fundamental arithmetic operations. To do so, however, we must first understand the multiplication and division fundamentals. For example, \(50\% \) can be written as \(\frac{{50}}{{100}}\) which can be simplified to \(\frac{1}{2}\) in fractional form, \(0.5\) in decimal form, \(1:2\) in ratio form. This article will discuss how to convert a percentage to a fraction, decimals, and ratio form.

Percentage

A percentage is a relative value is indicating the hundredth parts of any quantity.
The symbol used to represent the percent sign is \(“\% .”\)
A percent is a number with no dimensions and no units of measurement.
Examples: \(20\% ,\,64\% ,\,3.6\% ,\,…\)

Fraction

Fractions can be defined as the parts of a whole and are represented as numerical values. A fraction is a part or section of a whole that can be any number, a particular value, or object.
It means two in seven equal parts. It can also be read as:
two-seventh, or \(2\) by \(7\)
Mathematically a fraction is represented as \(\frac{2}{7}.\)

Decimal

A decimal point is a dot that separates the fractional part and whole number part in a decimal number. In decimal numbers, the fractional part is to the right of the decimal point, whereas integers or whole numbers are numbers to the left of the decimal point. If we start with the ones, the following decimal position will be \({\frac{1}{{10}}^{{\rm{th}}}}\) or one-tenth position.
Example: \(7.591\)

Ratio

The ratio is a comparison of two quantities of the same units that shows how much of one quantity is contained in the other.
The general form of expressing a ratio between two quantities, such as ‘\(m\)’ and ‘\(n,\)’ is \(m:n,\) which can be read as \(m\) is to \(n.\)
Examples: \(3:5,\,4:8.\)

Conversion of Percents to Fractions

The converting of a percent to a fraction is simple. It also depends on the percentage’s numerical value. The percentage’s numeric value can be a whole number, a fraction, or a decimal. The percentage symbol is removed in all circumstances, and the numeric value is divided by \(100.\) Let’s have a look at some of the following form-to-form conversions.

Conversion of Whole Number Percent to Fraction

To convert the whole number percent to a fraction, the following steps can be used:
Step 1: Remove the percent symbol and divide it by \(100.\)
Step 2: Reduce the fraction with \(100\) as the denominator into a simple fraction.
Example: If there are \(55\) girls out of \(100\) students in the class, we mean \(55\% \) are girls.
So, \(55\% = \frac{{55}}{{100}} = \frac{{11}}{{20}}\)

Conversion of Mixed Number Percent to Fraction

To convert mixed number percent to fraction, follow the steps given below:
Consider example \(3\frac{1}{4}\% .\)
Step 1: Convert it into an improper fraction.
\( \Rightarrow 3\frac{1}{4}\% = \frac{{13}}{4}\% \)
Step 2: Drop the per cent symbol \(\% ,\) multiplying by \(\frac{1}{{100}}.\)
\( \Rightarrow \frac{{13}}{4}\% = \frac{{13}}{4} \times \frac{1}{{100}} = \frac{{13}}{{400}}\)
Step 3: If it is possible, reduce it to the lowest form.

Convert Decimal Percent to Fraction

To convert decimal percent to fraction, follow the steps given below. Consider the percentage value of \(2.5\% .\)
Step 1: Drop the \(\% \) symbol and divide it by \(100.\) So, \(2.5\% = \frac{{2.5}}{{100}}.\)
Step 2: Drop the decimal point of the numerator.
Since only one decimal place is there, multiply both numerator and denominator by \(10.\)
\( \Rightarrow \frac{{2.5 \times 10}}{{100 \times 10}} = \frac{{25}}{{1000}}\)
Step 3: Reduce this fraction to its lowest form by finding the greatest common factor of the numerator and denominator.
\( \Rightarrow \frac{{25 \div 25}}{{1000 \div 25}} = \frac{1}{{40}}\)
Therefore, \(2.5\% = \frac{1}{{40}}.\)

Conversion of Percentage to Decimal

To convert percent to decimal, follow the steps given below.
Consider an example \(75\% \)
Step 1: Drop the \(\% \) symbol and divide it by \(100.\)
\( \Rightarrow 75\% = \frac{{75}}{{100}}\)
Step 2: Get the fraction’s numerator. Place the decimal point after two from right to left if the denominator of the given fraction is \(100.\)
\( \Rightarrow \frac{{75}}{{100}} = 0.75\)
Note: Add zeroes to the left of the numerator if the numerator contains fewer digits.

Converting Percentage to Ratio

Steps to convert percentage into a ratio are listed below.
Consider an example of \(35\% .\)
Step 1: Obtain the percentage.
Step 2: Convert the given percentage into a fraction by dividing it by \(100\) and removing the percentage symbol \(\left( \% \right).\)
\( \Rightarrow 35\% = \frac{{35}}{{100}}\)
Step 3: Reduce the obtained fraction in the previous step to the simplest form.
\( \Rightarrow \frac{{35}}{{100}} = \frac{7}{{20}}\)
Step 4: Write the obtained fraction in step 3 as a ratio.
\( \Rightarrow \frac{7}{{20}} = 7:20\)

Percent, Fraction, Decimal and Ratio chart

Percent	Fraction	Decimal	Ratio
\(35\% \)	\(\frac{7}{{20}}\)	\(0.35\)	\(7:20\)
\(65\% \)	\(\frac{{13}}{{20}}\)	\(0.65\)	\(13:20\)
\(33\% \)	\(\frac{1}{3}\)	\(0.33\)	\(1:3\)
\(25\% \)	\(\frac{1}{4}\)	\(0.25\)	\(1:4\)
\(80\% \)	\(\frac{4}{5}\)	\(0.8\)	\(4:5\)
\(60\% \)	\(\frac{3}{5}\)	\(0.6\)	\(3:5\)
\(956\% \)	\(\frac{{239}}{{25}}\)	\(9.56\)	\(239:25\)

Solved Examples: Converting Percentage to Fraction, Decimal, Ratio

Q.1. Convert \(5\% \) to decimal form.
Ans: Given \(5\% \)
We know,
\(5\% = \frac{5}{{100}}\)
Place the decimal point after two places from right to left because the denominator of the given fraction is \(100.\)
\( \Rightarrow \frac{5}{{100}} = 0.05\)
Therefore, \(5\% = 0.05.\)

Q.2. Express each of the following fraction percentages into a ratio in the lowest term:
1. \(\frac{3}{7}\% \)
2. \(\frac{5}{{12}}\% \)
3. \(\frac{3}{{25}}\% \)
Ans:
We know, first, remove the \(\% \) symbol and multiply it with \(\frac{1}{{100}}.\)
Then reduce the obtained fraction to the simplest form. At last, express it in ratio form.
1. \(\frac{3}{7}\% = \frac{3}{7} \times \frac{1}{{100}} = \frac{3}{{700}} = 3:700\)
2. \(\frac{5}{{12}}\% = \frac{5}{{12}} \times \frac{1}{{100}} = \frac{5}{{1200}} = \frac{1}{{240}} = 1:240\)
3. \(\frac{3}{{25}}\% = \frac{3}{{25}} \times \frac{1}{{100}} = \frac{3}{{2500}} = 3:2500\)
Therefore, \(\frac{3}{7}\% = 3:700,\,\frac{5}{{12}}\% = 1:240,\,\frac{3}{{25}}\% = 3:2500.\)

Q.3. Express \(40\% \) in ratio form.
Ans: Given \(40\% \)
We know,
Convert the given percentage into a fraction by dividing it by \(100\) and removing the percentage symbol \(\left( \% \right).\) Reduce the obtained fraction to the simplest form. Then, the simplest form of a fraction is to be expressed as a ratio.
\( \Rightarrow 40\% = \frac{{40}}{{100}} = \frac{2}{5} = 2:5\)
Therefore, \(40\% = 2:5.\)

Q.4. Express each of the following decimal percentages as ratios in the simplest form:
1. \(14.5\% \)
2. \(0.6\% \)
3. \(1.8\% \)
Ans:
We know,
Drop the \(\% \) symbol and divide it by \(100.\) And drop the decimal point of the numerator. Multiply both numerator and denominator by \(10.\) Then, reduce this fraction to its lowest form and represent it as a ratio.
1. \(14.5 = \frac{{14.5}}{{100}} = \frac{{14.5 \times 10}}{{100 \times 10}} = \frac{{145}}{{1000}} = \frac{{29}}{{200}} = 29:200\)
2. \(0.6 = \frac{{0.6}}{{100}} = \frac{{0.6 \times 10}}{{100 \times 10}} = \frac{6}{{1000}} = \frac{3}{{500}} = 3:500\)
3. \(1.8 = \frac{{1.8}}{{100}} = \frac{{1.8 \times 10}}{{100 \times 10}} = \frac{{18}}{{1000}} = \frac{9}{{500}} = 9:500\)
Therefore, \(14.5\% = 29:20\) and \(0.6\% = 3:50,\,1.8\% = 9:50.\)

Q.5. Express each of the following percentages into a fraction in lowest terms:
1. \(15\% \)
2. \(65\% \)
Ans: We know,
First, we need to drop the \(\% \) symbol and divide it by \(100.\) Drop the decimal point of the numerator. Reduce this fraction to its lowest form by finding the greatest common factor of the numerator and denominator.
1. \(15\% = \frac{{15}}{{100}} = \frac{3}{{20}}\)
2. \(65\% = \frac{{65}}{{100}} = \frac{{13}}{{20}}\)
Therefore, \(15\% = \frac{3}{{20}}\) and \(65\% = \frac{{13}}{{20}}.\)

Summary

The conversion of a percent to a fraction or other form of numbers is simple. It also depends on the percentage’s numerical value. The percentage’s numeric value can be a whole number, a fraction, or a decimal. The percentage symbol is removed in all circumstances, and the numeric value is divided by \(100.\) This article includes the definition of percent, fraction, decimals. This article, “Conversion of Percentage to Fraction, Decimals and Ratios,” help in understanding these in detail, and it helps solve the problems based on these very easily.

Frequently Asked Questions (FAQs) – Converting Percentage to Fraction, Decimal, Ratio

Q.1. How do you convert percents to ratios?
Ans: Steps to convert percentage into a ratio are listed below.
Step 1: Obtain the percentage.
Step 2: Convert the given percentage into a fraction by dividing it by \(100\) and removing the percentage symbol \(\left( \% \right).\)
Step 3: Reduce the obtained fraction in the previous step to the simplest form.
Step 4: Write the obtained fraction in step 3 as a ratio.

Q.2. How do you convert a decimal percentage to a fraction?
Ans: To convert decimal percent to fraction, follow the steps given below.
Step 1: Drop the \(\% \) symbol and divide it by \(100.\)
Step 2: Drop the decimal point of the numerator. Multiply both the numerator and denominator by \(10.\)
Step 3: Reduce this fraction to its lowest form by finding the greatest common factor of the numerator and denominator.

Q.3. How do you change a percent to a decimal?
Ans: To convert percent to decimal, follow the steps given below.
Step 1: Drop the \(\% \) symbol and divide it by \(100.\)
Step 2: Reduce this fraction to its lowest form by finding the greatest common factor of the numerator and denominator.
Step 3: Divide the numerator by the denominator to get the decimal.

Q.4. How do you convert a decimal percent to a decimal?
Ans: To convert decimal percent to decimal, follow the steps given below.
Step 1: Drop the \(\% \) symbol and divide it by \(100.\)
Step 2: Drop the decimal point of the numerator. Multiply both numerator and denominator by \(10.\)
Step 3: Reduce this fraction to its lowest form by finding the greatest common factor of the numerator and denominator.
Step 4: Divide the numerator by the denominator to get the decimal.

Q.5. What is the percentage in simple words?
Ans: Percent means out of one hundred. It is represented with the symbol \(\% .\)
Examples:
1. \(13\% = \frac{{13}}{{100}}\)
2. \(28\% = \frac{{28}}{{100}}\)