Decimal to Fraction
In this section, we will learn how to convert decimal to fraction. Before proceeding to conversion, take a quick look at decimal and fraction.
Decimal
A decimal number is a number that has a decimal point (.). The decimal part separates the whole number and decimal part. It is a way to represent a fraction. It is not a whole number. For example, 23.56, 0.667, 1234.09877, etc.
If a decimal number has any number of zeros after the decimal point, consider it as a whole number. Because zeros after decimal point do not affect the value. For example, 78.0000 is the same as 78. But 78.00001 is not the same as 78.
Let’s have a look at the following decimal place value chart.
In the above table, we have observed that when we move to the left of the decimal point the values get 10 times larger, and moving to the right of decimal point the values get 10 times smaller.
Let’s take a decimal number and understand what does it mean.
Fraction
A fraction represents the decimal number in the form of numerator and denominator, i.e.
. It is a way to express the decimal numbers. It is also known as a rational number. There are two types of fractions:
- Improper Fraction
- Mixed Fraction
Improper Fraction
A fraction that is in the form of and numerator is greater than the denominator is called an improper fraction. For example,
.
Mixed Fraction
A mixed fraction is a fraction that is in the form of a
where, a is the whole number and is the fractional part.
Decimal to Fraction Conversion
To convert decimal to fraction, follow the steps given below.
Step 1: Write down the decimal number which you want to convert, and divide it by 1.
Step 2: Remove the decimal point. To achieve the same, multiply the numerator and denominator by the same number. If there is one digit after the decimal point, multiply by 10. If there are two digits after the decimal point, multiply by 100. Similarly, if there are three digits after the decimal point, multiply by 1000, and so on.
Step 3: Simplify (reduce) the fraction, if required.
Note: While simplifying the fraction remember that numerator and denominator must be divisible by the same number.
Let’s understand it through examples.
Example 1: Change the decimal number 0.5 to a fraction.
Solution:
Step 3: On simplifying the fraction
, we get:
Hence, 0.5 is in fraction.
Example 2: Change the decimal number 0.77 to a fraction.
Solution:
Step 3: We cannot simplify the fraction
.
Hence, 0.77 isin fraction.
Example 3: Change the decimal number 9.275 to a fraction.
Solution:
Step 3: On simplifying the fraction
, we get:
Hence, 9.275 isin fraction.
Example 4: Change the decimal number 0.625 to a fraction.
Solution:
Step 3: Reduce the fraction
. Divide the numerator and denominator by 25, we get
. We can also reduce the fraction. Divide numerator and denominator by 5, we get
.
Therefore, on simplifying the fraction, we get:
Hence, 0.625 isin fraction.
Example 5: Change the decimal number 2.98 to a fraction.
Solution:
Step 3: Reduce the fraction
. Divide the numerator and denominator by 2, we get
.
Hence, 2.98 isin fraction.
When a decimal number has the whole number part
Step 1: Ignore the whole number for a moment.
Step 2: Write down the remaining decimal number which you want to convert, and divide it by 1.
Step 3: Remove the decimal point. To achieve the same, multiply the numerator and denominator by the same number, as we have seen above.
Step 4: Simplify (reduce) the fraction, if required.
Step 5: After that, write the whole number (that we have ignored above) along with the fraction part.
Let’s understand through the example.
Example 6: Change the decimal number 2.98 to a fraction.
Solution:
Step 1: 0.98
Step 4: Reduce the fraction
. Divide the numerator and denominator by 2, we get
.
Step 5: 2
Hence, 2.98 is 2 in mixed fractions.
Example 7: Change the decimal number 13.6755 to a fraction.
Solution:
Step 1: 0.6755
Step 4: Reduce the fraction
. Divide the numerator and denominator by 5, we get
.
Step 5: 13
Hence, 13.6755 is 13 in mixed fractions.