How to Convert Percents, Fractions and Decimals: Step-By-Step Guides

Rosemary September 14, 2021 | 01:21

Percents, fractions, and decimals are all just different ways of writing numbers. This article will show you how to convert percents, fractions, and decimals with simple steps.

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What is Percentage?

Percentage is a term from Latin, meaning ‘out of one hundred’.

You can therefore consider each ‘whole’ as broken up into 100 equal parts, each one of which is a single percent.

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The term ‘per cent’ means ‘out of a hundred’. In mathematics, percentages are used like fractions and decimals, as ways to describe parts of a whole. When you are using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage, and less commonly the abbreviation ‘pct’ may be used.

What is Fraction?

Fractions represent equal parts of a whole or a collection.

Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.

For example,

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Fraction of a collection: Fractions also represent parts of a set or collection.

For example,

There are total of 5 children.

3 out of 5 are girls. So, the fraction of girls is three-fifths ( 3⁄5 ).

2 out of 5 are boys. So, the fraction of boys is two-fifths ( 2⁄5 ).

A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.

What is Decimal?

A decimal number system is used to express the whole number and fraction together. Here, we will separate the whole number from the fraction by inserting a ".", which is called a decimal point. For example, let's say you are going to take a cone of ice cream. The vendor tells you that the price of ice cream is $2 and 50 cents. Now, if you want to express this whole amount in one figure, you will say that the price of the ice cream cone is $2.50. There are many such real-life situations in which you might be using decimals without even realizing it. Let us understand the concepts of decimals in a clear way with the help of this article.

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Reading Decimal Numbers: There are two ways to read a decimal number. The first way is to simply read the whole number followed by "point", then to read the digits in the fractional part separately. It is a more casual way to read decimals. For example, we read 34.56 as thirty-four point fifty-six. The second way is to read the whole number part followed by "and", then to read the fractional part in the same way as we read whole numbers but followed by the place value of the last digit. For example, we read 34.56 as thirty-four and fifty-six hundredths.

Writing Decimals

Let us understand this with an example. We have to write the number 123.456 as words. The above decimal number can be written in words as, One hundred twenty-three and four-hundredth fifty-six thousandth, or one hundred twenty-three point four five six. For example, let us try to find out how the decimal number 85.64 can be written in words.

Comparing Decimals

In order to compare the decimals, keep the following two things in mind. First, compare the digits before the decimal point, if they are less than or greater than the other number, then it is greater than or less than respectively the other number. Second, if the digits before the decimal point are equal to each other then we compare the first digit after the decimal point which is the tenth digit, and examine which is greater or smaller. We repeat this process and keep on comparing digits to the right until we get the unequal digits.

For example, let's compare 23.789 with 23.759. Here we see digits before the decimal point are equal which is 23 = 23. Now moving on to the tenths digits to compare. i.e., 23.789 with 23.759, we get 7 = 7. Both of them are equal. Now we move to the next term to the right of the tenths digit which is the hundredth digit. i.e., 23.789 with 23.759. Now, since 8>5, then we can say that 23.789 > 23.759. ∴ 23.789 > 23.759.

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Converting Percent to Decimal

To convert from percent to decimal divide by 100 and remove the % sign.

An easy way to divide by 100 is to move the decimal point 2 places to the left:

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Don't forget to remove the % sign!

Converting Decimal To Percent

Move the decimal point 2 places to the right

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Don't forget to add the % sign!

From Fraction to Decimal

To convert a fraction to a decimal divide the top number by the bottom number:

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Example: Convert

2/5 to a decimal

Divide 2 by 5: 2 ÷ 5 = 0.4

Answer:

2/5 = 0.4

From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

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From Fraction to Percentage

To convert a fraction to a percentage divide the top number by the bottom number, then multiply the result by 100%

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Example: Convert

3/8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375

Then multiply by 100%: 0.375 × 100% = 37.5%

Answer:

3/8 = 37.5%

From Percentage to Fraction

Move the decimal point two places to the left to convert a percent to a decimal. Unless otherwise noted, in a percent, the decimal point comes at the end of the last number. For example, envision that 75% actually looks like 75.0%. Moving the decimal point two places to the left converts the percent to a decimal. This is the same thing as dividing the number by 100.

Examples:

75% converts to .75

3.1% converts to .031

0.5% converts to 0.005

Express the percent as a fraction of 100. Writing a number as a fraction of 100 is simply another way to write a perce. The number of the percent becomes the numerator of the fraction and 100 becomes the denominator. Simplify the fraction to its lowest form.

Example: 36% turns to 36/100.

To simplify, look for the highest number that goes into 36 and 100. In this case, that would be 4.

Determine how many times 4 goes into 36 and 100. When you simplify, the answer would be 9/25.

To check that you’ve converted correctly, divide 9 by 25 (0.36) and multiply by 100 (36%). This number should equal your original percent.