Decimal to Fraction Formula: Simple Conversion Method

To convert a decimal to a fraction , we begin by expressing the given decimal as a fraction, initially with a denominator of 1. Then, we proceed to eliminate the decimal point (.) by multiplying both the numerator and denominator by powers of 10. For instance, if we have the decimal 1.9, we convert it to the equivalent fraction 19/10. It's important to note that we can't further simplify 19/10.

Decimal: In the context of computers, decimal numbers are those with a base of 10. However, in mathematics, a decimal number is one that contains a dot (.) or decimal point within its digits. Essentially, decimals can be thought of as fractions where the denominators are 10 or multiples of 10. Examples of decimals include 3.2, 10.9, 55.1, 1.28, 9.234, and so on.

Fractions are mathematical expressions that represent parts of a whole number. They are typically denoted as a ratio of two integers, a/b, where 'a' is the numerator and 'b' is the denominator. Importantly, the denominator (b) must not be equal to zero. Fractions allow us to express the division of a quantity into smaller, equal parts. For example, 1/2 represents one-half of something, and 3/5 represents three-fifths of a whole.

Arithmetic operations, such as addition, subtraction, multiplication, and division, can be performed on fractions, allowing us to work with fractional quantities in various mathematical contexts.

How to Convert Decimal into Fractions?

Certainly, here are the steps to convert a decimal into a fraction:

Write the Decimal as a Ratio: Begin by expressing the given decimal as a ratio in the form p/q, where 'p' is the decimal number, and 'q' is 1. For example, if you have the decimal 0.75, you would write it as 75/1.

Multiply by Powers of 10: Next, you need to eliminate the decimal point by multiplying both the numerator and the denominator by a suitable power of 10. The power of 10 should be chosen based on the number of decimal places. For example:

If there is one decimal place (e.g., 0.7), multiply by 10 to get 7/10.

If there are two decimal places (e.g., 0.25), multiply by 100 to get 25/100.

Simplify the Fraction: After multiplying by the appropriate power of 10, simplify the resulting fraction, if possible. This means finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it to reduce the fraction to its simplest form. In the examples above, 7/10 can be simplified to 3/5, and 25/100 can be simplified to 1/4.

By following these steps, you can convert a decimal into a fraction. This process is particularly useful when you need to work with fractional values or compare decimals to fractions.

Solved Examples

Question 1: Find the fraction form of the decimal 0.7.

Solution:

Given decimal: 0.7.

To convert to a fraction, we write it as 7/10.

We can also find equivalent fractions by multiplying both the numerator and denominator by the same number. For example:

Multiplying 7/10 by 2 gives 14/20.

Multiplying 7/10 by 5 gives 35/50.

Multiplying 7/10 by 10 gives 70/100.

So, the fractions equivalent to 0.7 are 7/10, 14/20, 35/50, and 70/100.

Question 2: Convert 7.15 into a fraction.

Solution:

Given decimal: 7.15.

To convert to a fraction, multiply by 100 to get 715/100.

Simplifying further, we can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case, to get 143/20.

Another equivalent fraction can be found by multiplying both the numerator and denominator by 2, resulting in 286/40.

So, the fractions equivalent to 7.15 are 715/100, 143/20, and 286/40.

Also Check – Congruence of triangles formula

Question 3: Convert 3.35 into a fraction.

Solution:

Given decimal: 3.35.

To convert to a fraction, we write it as 335/100.

This can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case, to get 67/20.

So, the fraction equivalent to 3.35 is 67/20.

Question 4: Convert 1.625 into a mixed fraction.

Solution:

Given decimal: 1.625.

To convert to a fraction, we write it as 1625/1000.

Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 125 in this case, we get 13/8.

Finally, we can express this fraction as a mixed fraction, which is 1 5/8.

Hence, 1.625 is equivalent to the mixed fraction 1 5/8.

Also Check – Line and Angles Formula

Repeating Decimal to Fraction

Converting a regular decimal number into a fraction is a straightforward process, but when dealing with repeating or recurring decimals, the conversion can be more involved. Repeating decimals are numbers that have a recurring pattern, such as 0.666..., 4.17777..., or 0.56111.... Let's explore how to convert a repeating decimal to a fraction using an example.

Example: Convert the repeating decimal 0.6666... into a fraction.

Solution:

Let x be = 0.6666

Now multiply x by 10 on both sides.

10 x = 6.666…

Subtracting x from 10x,

10x-x = 6.666…-0.6666

9x = 6.000

x = 6/9 = ⅔

Also Check – Line and Angles Formula

Decimal to Fraction Table