Conversion of Fraction and Decimal to Percentage: Fractions, decimals and percents are three different ways to express any number, but as the base value is always a hundred, the percentage is used for comparing different values. The most important and basic operations are converting fractions to decimals, fractions to percentages and vice-versa. To do so, we must first master the fundamentals of multiplication and division. For example, \(\frac{3}{6}\) is a fraction if we divide numerator by denominator gives \(0.5\) in the decimal form its percentage form is \(50\% .\)

We will convert fractions and decimals to percentages and fractions to decimals after we learn this.

Fractions

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 four in five equal parts. It can also be read as:
Four-fifth, or \(4\) by \(5\)
Mathematically represented as \(\frac{4}{5},\) it is called a fraction.
Example:

Decimals

A decimal point is a dot consisting of two parts of numbers called a decimal. Integers or whole numbers are numbers to the left of the decimal point, whereas fractional parts are to the right of the decimal point. If we start with the ones, the following position will be \(\frac{{{1^{{\text{th}}}}}}{{10}}\) or one-tenth position.
Example: \(17.591\)

Percentage

A percentage is a number or ratio expressed as a fraction of \(100\) in mathematics. The per cent sign, “\( \% ,\)” is frequently used. A per cent is a number with no dimensions and no units of measurement.
Examples: \(10\% ,34\% ,…\)

Conversion of Fraction to Decimal

1. The two parts in a fraction are a numerator and a denominator. It is used to represent the number of parts we have compared to the total number.
Example: \(\frac{3}{6}\)
Here, \(3 \to \) numerator, \(6 \to \) denominator
2. In a fraction, the division symbol is represented by a line that separates the numerator and denominator.
3. To convert a fraction to a decimal, divide the numerator by the denominator. As a result, we will get a decimal result.
Example: \(\frac{2}{4} = 0.5\)

Convert Mixed Fraction to Decimal

Converting a mixed fraction to a decimal can be done in two ways:
1. After converting the mixed fraction to an improper fraction, divide the improper fraction.
Example: \(3\frac{1}{4} = \frac{{13}}{4} = 3.25\)
2. Only convert the fractional part to the decimal part, then add it to the whole number. To put it another way, maintain the full number the same while converting the fraction.
Example: \(3\frac{1}{4} = 3 + \frac{1}{4} = 3 + 0.25 = 3.25\)

Example: Change \(5\frac{2}{4}\) to decimal form.

We can write \(5\frac{2}{4}\) as \(5 + \frac{2}{4}\)
First, convert \(\frac{2}{4}\) into decimal form.
\( \Rightarrow \frac{2}{4} = \frac{{2 \times 25}}{{4 \times 25}} = \frac{{50}}{{100}} = 0.50\)
Now, \(5 + \frac{2}{4} = 5 + 0.5\)
\( \Rightarrow 5 + \frac{2}{4} = 5.5\)

Convert Fractions to Decimals If the Denominators are 10, 100,…

The following steps are used to convert fractions with denominators of \(10,100,1000,\) and so on into decimal numbers:

Step 1: If the fraction does not have a denominator of \(10,100,1000,\) or any other number, convert it to an equivalent fraction having a denominator of \(10\) or \(100\) or \(1000.\)

Step 2: Get the fraction’s numerator. Place the decimal point after one, two, or three places from right to left if the denominator of the given fraction is \(10\) or \(100\) or \(1000.\)

Note: Add zeroes to the left of the numerator if the numerator contains fewer digits.
Example: \(\frac{7}{{10}} = 0.7\)

Conversion of Decimal to Fractions

To convert any decimal to a fraction, follow these four steps.
Step 1: Find the place value of the digits in the number after the decimal.
Step 2: Use this information to find out what the fraction’s denominator would be. The powers of \(10\) in the denominator will be decided by the number of decimal places in the numerator.
Step 3: Remove the decimal point. Simplify it by writing it in fraction form.
Step 4: Express your solution of the lowest equivalent fraction.

Example: Convert \(0.4\) into a fraction.
\( \Rightarrow 0.4 = \frac{4}{{10}} = \frac{2}{5}\)

Conversion of Decimal to Percentage

Decimals and percents are two ways to express any number, but as the base value is always a hundred, the percentage is used for comparing different values.
Let’s have a look at the two simple steps for changing decimals to percentages.
Step 1: Shift the decimal point to the right by two places to multiply the number by \(100.\)
Step 2: Put in the per cent sign (per cent).

Example: \(0.45 = 0.45 \times 100 = 45\% \)

Conversion of Percentage to Decimal

To convert a per cent to a decimal, divide it by \(100\) and remove the per cent sign.
OR
We can convert per cent to a decimal by first converting it to a fraction and then rewriting it as a decimal.

Example: \(36\% = \frac{{36}}{{100}} = 0.36\)

Conversion of Fractions to Percentage

There are two methods to convert fraction to percentage:
Method -1:
Steps to Convert a Fraction to a Percent:
1. Divide the numerator by the denominator to convert a fraction to a decimal. The decimal is then multiplied by \(100\) to get per cent.
2. To convert a fraction to a decimal, divide the numerator by the denominator. Then, add the \(\% \) symbol to the obtained answer.

Example-1: Convert \(\frac{4}{{10}}\) into per cent.
Divide the numerator by the denominator.
So, \(\frac{4}{{10}} = 0.4\)
Then, multiply \(0.4\) with \(100.\) Then, add the \(\% \) symbol to the obtained answer.
\( \Rightarrow 0.4 \times 100 = 40\% \)
\( \Rightarrow \frac{4}{{10}} = 40\% \)

Example-2: Convert \(\frac{{60}}{{100}}\) to decimal form.
Divide the numerator by the denominator.
So, \(\frac{{60}}{{100}} = 0.6\)
Then, multiply \(0.6\) with \(100.\) Then, add the \(\% \) symbol to the obtained answer.
\( \Rightarrow 0.6 \times 100 = 60\% \)
\( \Rightarrow \frac{6}{{10}} = 60\% \)
Method -2:
To convert a fraction to a percentage, multiply it by \(100\) and add the per cent symbol to the end of the product.
Example-1: Convert \(\frac{{35}}{{100}}\) into per cent.
\(\Rightarrow \frac{{35}}{{100}} \times 100 = 35\% \)
Example-2: Convert \(\frac{1}{4}\) into per cent.
\( \Rightarrow \frac{1}{4} \times 100 = \frac{{25}}{1} = 25\% \)

Representation of Conversion of Fraction and Decimal to Percentage

Fraction, Decimal and Per cent Chart

Fraction	Decimal	Percent
\(\frac{1}{2}\)	\(0.5\)	\(50\% \)
\(\frac{3}{4}\)	\(0.75\)	\(75\% \)
\(\frac{1}{3}\)	\(0.33\)	\(33.3\% \)
\(\frac{1}{4}\)	\(0.25\)	\(25\% \)
\(\frac{35}{50}\)	\(0.7\)	\(70\% \)
\(\frac{3}{5}\)	\(0.6\)	\(60\% \)
\(\frac{956}{100}\)	\(95.6\)	\(956\% \)

Solved Examples – Conversion of Fraction and Decimal to Percentage

Q.1. Convert \(\frac{{25}}{{50}}\) to decimal form.
Ans: Given: \(\frac{{25}}{{50}}\)
Multiply both the numerator and the denominator by \(2\) to make the denominator \(100.\)
So, we have, \(\frac{{25}}{{50}} = \frac{{25 \times 2}}{{50 \times 2}} = \frac{{50}}{{100}}\)
We know,
Place the decimal point after two places from right to left because the denominator of the given fraction is \(100.\)
\( \Rightarrow \frac{{50}}{{100}} = 0.50\)
Therefore, \( \Rightarrow \frac{{25}}{{50}} = 0.5\)

Q.2. Convert \(\frac{2}{5}\) into per cent.
Ans: Given: \(\frac{2}{5}\)
We know,
To convert a fraction to a percentage, multiply it by \(100\) and add the per cent symbol to the end of the product.
\( \Rightarrow \frac{2}{5} \times 100 = \frac{{2 \times 20}}{1} = 40\% \)
Therefore, \(\frac{2}{5} = 40\% .\)

Q.3. Convert 0.375 as a fraction?
Ans: Given: \(0.375\)
\(0.375 = \frac{{375}}{{1000}} = \frac{{17}}{{40}}\)

Q.4. Change \(6\frac{1}{4}\) to decimal form.
Ans: We can write \(6\frac{1}{4}\) as \(6 + \frac{1}{4}\)
First, convert \(\frac{1}{4}\) into decimal form.
So, \(\frac{1}{4} = \frac{{1 \times 25}}{{4 \times 25}} = \frac{{25}}{{100}} = 0.25\)
Hence, \(6 + \frac{1}{4} = 6 + 0.25 = 6.25\)
Therefore, \(6.25\) is the decimal form \(6\frac{1}{4}.\)

Q.5. Convert 0.00198 to a fraction.
Ans: Given decimal fraction is \(0.00198.\)
To convert 0.00198 into a fractional number, first, we need to write in the numerator \(198,\) leaving out the decimal point and then write \(100000\) in the denominator since there are five digits after the decimal point.
Therefore, \(0.00198 = \frac{{198}}{{100000}} = \frac{{99}}{{50000}}.\)

Summary

Conversion of fractions and decimals to percentages are very important and interesting topics to learn in mathematics. To convert a fraction to a decimal, divide the numerator by the denominator. As a result, we will get a decimal. To convert a fraction to a per cent, divide the numerator by the denominator. Afterwards, the decimal is multiplied by \(100.\)

Per cent to decimal conversions are easy. We move the decimal point two places to the right. This article includes the definitions of fractions, decimals and percentages and these conversion steps, examples and problems.

Frequently Asked Questions (FAQs)

Q.1. How do you convert fractions to decimals?
Ans: Divide the numerator by the denominator to convert a fraction to a decimal. We can do this with a calculator if required. As a result, we will have a decimal answer.

Q.2. How do you change a fraction to a per cent?
Ans: Divide the numerator by the denominator to convert a fraction to a decimal. The decimal is then multiplied by \(100\) to get per cent.

Q.3. What are ratio, decimal, and per cent?
Ans: A ratio in mathematics indicates the number of times one number contains another.
Example: If a bowl of fruit contains eight oranges and six lemons,
The ratio of oranges to lemons is given by,
\(8:6 \Rightarrow 4:3\)
A decimal number is defined as a decimal point separating the full number and fractional parts. A decimal point is a dot in a decimal number. The digits after the decimal point represent a value less than one
A percentage is a number or ratio expressed as a fraction of a hundred (from Latin per centum “by a hundred”). A percentage is a dimensionless (pure) number that does not have a unit of measurement.

Q.4. What is \(\frac{7}{8}\) as a percentage?
Ans: We can easily solve this problem by converting the fraction \(\frac{7}{8}\) to a decimal first. To do so, divide the numerator by the denominator as follows:
\( \Rightarrow \frac{7}{8} = 0.875\)
Once we get the solution to that division, we can convert it to a percentage by multiplying it by \(100:\)
\( \Rightarrow 0.875 \times 100 = 87.5\% \)

Q.5. What is \(\frac{5}{8}\) as a percentage?
Ans: First, we can convert the fraction \(\frac{5}{8}\) to a decimal first. To do so, divide the numerator by the denominator as follows:
\( \Rightarrow \frac{5}{8} = 0.625\)
Once we get the solution to that division, we can convert it to a percentage by multiplying it by \(100:\)
\( \Rightarrow 0.625 \times 100 = 62.5\% .\)

We hope this detailed article on the conversion of fractions and decimals to percentage helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!