Percent To Decimal Or Fraction Conversion

Conversions are never easy. But they are very important in the calculation. While solving maths, you might have encountered many conversions. From meter to a kilometre, feet to the inch, gram to kilogram, and many more. All these conversions depend on the type of data given in the question and the answers required. The questions asked in the percentage can become a lot easier when you know the rules for converting percent to fraction. This will make the solution a lot easier.

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What is Percent to Fraction?

When you convert the given percentage into fraction it is called percent to fraction. We all know that percentage means ‘out of a hundred’. So to convert the percent to fraction initially you need to change the percentage to a decimal and then from decimal, you can convert it into a fraction. This will simplify the process.

For example, suppose the percentage given is 25%. So, in decimal, this will be 0.25. Now, 0.25 can also be written as 25/100 which is equal to 1/4. The easier way to remember this is whenever a digit is given and it is followed by percentage than place the decimal at two places from the left. The reason for following this approach is that you will be able to know how many zeroes you need to put in the denominator.

For example, you need to find the fraction of 106%. You will start with the placing the decimals. This will become 1.06. So you have determined that you need to put two zeroes in the denominator. So, it will become 106/100 = 53/50. This will be your final answer. Now, we will have more complex examples.

Suppose you need to find a fraction of 0.6%. So it’s decimal will be 0.006 which is equal to 6/1000 = 3/500. Remember that here you were asked to find the fraction of a decimal number. Because of using decimals first you had the idea beforehand about the number of zeroes in the denominator.

Browse more Topics Under Percentages

• Percent to Decimal or Fraction Conversion
• Percentage of Quantity
• Inverse Case – Value From Percentage
• Percentage Change
• Relative Percentage
• Product Constancy
• Consecutive Increments
• Consecutive Decrease
• Problems Based on Population
• Results on Depreciation
• Percentages Practice Questions

Fractions to Percentage

Let’s convert 4/5 to a percentage. Percentage always has 100 as the base. So you need to find the number with which when we multiply 5 it will become 100. That number is 20. So multiply 20 in the denominator as well as the numerator. So the fraction will become 4 x 20/5 x 20 = 80/100 = 80%. So, 80% is your required answer.

Convert 12/25 into a percentage. In this question also you need to make the base as 100 first and then you can convert the given digits into a percentage. When you multiply 25 by 4 it becomes 100. So multiply 4 in the numerator as well as the denominator. This will become, 12 x 4/25 x 4 = 48/100 = 48%.

The below table shows the value of percentage when you convert it from the fraction. You can remember this table to solve any fractions related questions.

	1	2	3	4	5	6	7	8	9	10	11	12
1	100
2	50	100
3	33.33	66.66	100
4	25	50	75	100
5	20	40	60	80	100
6	16.66	33.33	50	66.66	83.33	100
7	14.28	28.57	42.85	57.14	71.42	85.71	100
8	12.5	25	37.5	50	62.5	75	87.5	100
9	11.11	22.22	33.33	44.44	55.55	66.66	77.77	88.88	100
10	10	20	30	40	50	60	70	80	90	100

What is the use of this table?

You will notice that the values given in the table are only percentage values. You can easily convert this values into decimals by shifting two places to the left. Thus, 66.66% = 0.6666 in decimal value. Another use of this table is that in the process of division by any number such as 2, 3, 4, 5, 6, 7, and so on, candidates normally face difficulty in calculating the decimal values of these divisions.

However, when you get used to the decimal values that are in the table, calculations will become a lot easier. For example, when you divide an integer by 7, the decimal values can only be 0.14, 0.28, 0.42, 0.57, 0.71, 0.85 , or 0.00.
This also denotes that the difference between two ratios like x/4 – x/5 is integral only when x is divisible by 4 as well as 5.

Solved Example

Q. What is the percentage value of the ratio 53/81?

In this question, to find the answer you need to remove all the 50%, 100%, 10%, 1%, and all such of the denominator from the numerator.

53/81 will be written as :

  (40.5 + 12.5)/81 = 40.5/81 + 12.5/81 = 50% + 12.5/81
= 50% + (8.1 + 4.4)/81 = 50% + 10% + 4.4/81
= 60% + 4.4/81

So, now we have established that answer is somewhere between 60 and 70 %. You need to find those remaining digits now. This can be found by calculating 4.4/81 through the normal process of multiplying the numerator by 100.

So, the % value of 4.4/81 = 4.4 x 100/ 81 = 440/81. 440/81 will be 5% with 35 as a remainder.
To find the remaining digits, add a zero to the remainder and divide it by 81. Here, that remainder is 35. It will become 350/81 = 4 with 26 as a remainder. Again repeat the process for 260/81 with 3 and remainder as 17. So the final answer will be 65.43.

Practice Questions

Q. What will be the percentage value of the ratio 223/72?

A. 308.5 %         B. 309.52 %         C. 309.72 %           D. 309.83 %

Ans: The correct answer is C.

Q. What will be the percentage value of the ratio of 53/14?

A. 378.57 %         B. 378.75 %         C. 380 %           D. 383 %

Ans: The correct answer is A.

 Q. Calculate 123 x 4.73.

A. 582.67         B. 582.5         C. 580           D. 581.79

Ans: The correct answer is D.