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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.

Decimal to Fraction

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.

Decimal to Fraction

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.

Decimal to Fraction

Fraction

A fraction represents the decimal number in the form of numerator and denominator, i.e.Decimal to Fraction. 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 Decimal to Fraction and numerator is greater than the denominator is called an improper fraction. For example,Decimal to Fraction.

Mixed Fraction

A mixed fraction is a fraction that is in the form of aDecimal to Fraction where, a is the whole number and Decimal to Fraction 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.

Decimal to Fraction

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:

Decimal to Fraction

Step 3: On simplifying the fractionDecimal to Fraction, we get:Decimal to Fraction

Hence, 0.5 is Decimal to Fraction in fraction.

Example 2: Change the decimal number 0.77 to a fraction.

Solution:

Decimal to Fraction

Step 3: We cannot simplify the fractionDecimal to Fraction.

Hence, 0.77 isDecimal to Fractionin fraction.

Example 3: Change the decimal number 9.275 to a fraction.

Solution:

Decimal to Fraction

Step 3: On simplifying the fractionDecimal to Fraction, we get:Decimal to Fraction

Hence, 9.275 isDecimal to Fractionin fraction.

Example 4: Change the decimal number 0.625 to a fraction.

Solution:

Decimal to Fraction

Step 3: Reduce the fractionDecimal to Fraction. Divide the numerator and denominator by 25, we getDecimal to Fraction. We can also reduce the fractionDecimal to Fraction. Divide numerator and denominator by 5, we getDecimal to Fraction.

Therefore, on simplifying the fractionDecimal to Fraction, we get:Decimal to Fraction

Hence, 0.625 isDecimal to Fractionin fraction.

Example 5: Change the decimal number 2.98 to a fraction.

Solution:

Decimal to Fraction

Step 3: Reduce the fractionDecimal to Fraction. Divide the numerator and denominator by 2, we getDecimal to Fraction.

Hence, 2.98 isDecimal to Fractionin 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.

Decimal to Fraction

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

Decimal to Fraction

Step 4: Reduce the fractionDecimal to Fraction. Divide the numerator and denominator by 2, we getDecimal to Fraction.

Step 5: 2Decimal to Fraction

Hence, 2.98 is 2Decimal to Fraction in mixed fractions.

Example 7: Change the decimal number 13.6755 to a fraction.

Solution:

Step 1: 0.6755

Decimal to Fraction

Step 4: Reduce the fractionDecimal to Fraction. Divide the numerator and denominator by 5, we getDecimal to Fraction.

Step 5: 13 Decimal to Fraction

Hence, 13.6755 is 13 Decimal to Fraction in mixed fractions.






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