Ratio to Percentage

Let us recall the meaning of the ratio. A ratio is a comparison of two similar quantities. Given any two similar quantities a and b, the ratio of a to b that is a:b is defined as a:b = a/b, where b≠0. 

Percentage means ‘by the hundred’ or ‘divide by one hundred’. The percentage is also used to compare quantities, which means ‘per 100’. So when you say 100% of something, it means you are talking of the whole.

Percentages are similar to ratios, but a specific type of ratio. Percentages compare any one part against the whole, instead of comparing two parts of the whole against each other. The ratio to percentage conversion process helps to represent a number in ratio form to percentage form.

In this article let us study how to convert the ratio to percentage.

Ratio

If a and b are two different numbers or integers, then the ratio of these two integers can be represented as a/b or a:b. 

We can say that the comparison of two quantities of the same kind is referred to as a ratio. This relation gives us how many times one quantity is equal to the other quantity. In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones.

The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:. 

For example, A ratio can be written as a fraction, say 3/2, or can be represented by using “is to”, as “3 is to 2.” 

Percentage

A percentage is a part of the whole. The percentage formula is used to find the amount or share percentage of something in terms of the whole (100%). Percent means per hundred. The percentage is denoted by the symbol ‘%’, the percentage is majorly used to compare and find out ratios.

Now let us study the steps for how to convert the ratio to percentage.

How to Convert Ratio to Percentage

Converting Ratios Into Percentages

When you want to turn a ratio into a percentage, you must just take one part to compare against the whole. For example, you could find out the percentage of a student in semester one in the following steps:

The given ratio is 586: 600

Step 1: Write a new fraction

First, obtain the given ratio and convert it into a fraction.

Because percentages compare one part against the whole, you can write the total marks of a student scored in the examination with the total number of marks.

We have,

586 (total marks scored) / 600  ( total marks)

It could also be written as 586 : 600

Here you're comparing one part against the whole.

Step 2: Work the Division

Divide the fraction.

586 ÷ 600

= 0.9766666

Rounding up

= 0.98

Step 3: Convert the Decimal to a Percentage

Multiply the result of Step 2 by 100 to convert it into a percentage.

0.98 × 100 = 98%

So the student scored 98% in semester one.

As now we are familiar with ratio to percentage conversion, let us study ratio and percentage questions.

Ratio To Percentage Formula

The Ratio to Percentage Formula is given as,

Solved Examples:

Example 1: The angles of a triangle are in the ratio 1:2:3. Find the measures of each angle. What will be the percentage of each angle?

Solution:

Given that the angles are in the ratio 1: 2 : 3

The total part will be 1 + 2 + 3 = 6

For finding the measures of the angle we have to multiply the fraction by 180 as a total measure of the triangle is 1800

Thus, the measure of the first angle = 1/6 x 180 = 300

Measure of the second angle = 2/6 x 180 = 600

Measure of the third angle = 3/6 x 180 = 900

Now let us convert the ratio to the percentage we have,

First angle = 1/6 x 100% = 16.66%

Second angle =2/6 x 100% = 33.33%

Third angle = 3/6 x 100% = 50%

Example 2: There are 90 students in a class. Out of them, 30 are girls. Find the percentage of girls in the class?

Solution:

The given ratio is 30:90 = 30/90

Percentage of girls in a class = Ratio x 100%

= 30/90 x 100

= 0.34 x 100

= 34%

Therefore there are a total of 34% girls in the class.

Example3: What are the steps to convert the ratio 5: 4 into percentage?

Step 1: The ratio 5:4 is written as 5/4.

Step: On dividing the fraction 5/4, we get 1.25

Step 2: On multiplying 1.25 by 100 , we get 125.

Step 3: Adding  the percentage symbol (%) to the resultant value, we get 125%.

The ratio 5:4 is written as 125%.

Example 4: Convert the ratio 2:4 into a percentage.

Solution:

Given ratio: 2:4

Step 1: The ratio 2:4 is written as 1/2.

Step 2: On dividing the fraction 1/2 we get 0.5

Step 3: On multiplying 0.5 by 100 , we get 50

Step 3: Adding the percentage symbol to the resultant value, we get the answer as 50%.

Therefore, 2:4 = 250%.

Example 5: Varun received his monthly salary. The ratio of his expenditure to savings is 7:3. What percentage of his salary did he spend, and what percentage was saved by him?

Solution:

Since the part of savings and expenditures are 3 and 7, the salary can be taken as 3 + 7 = 10 parts. This implies, 7/10 part of the salary is spent whereas 3/10 parts are saved.

Converting ratio to percentage we get,

Percentage of expenditure = 7/10 x 100% = 70%

Similarly, percentage of savings = 3/10 x 100% = 30%