**Decimals**

**Conversion: Fractions to Decimals, Decimals to Fractions**

- A fraction is the number expressed as the numerator divided by the denominator.
- Example:
2 / 3,5 / 2, etc.
- A decimal is the number in which the whole number part and the fractional part are expressed together.
- Example: 0.523, 1.978, etc.

Method to convert fractions to decimals

- By converting the denominator to the power of 10, i.e., 10, 100, 1000, etc.
- Long division method.

Converting the denominator to the power of 10

- Think about the number which when multiplied by the denominator gives the number that is in the power of 10.
- Multiply the numerator and the denominator of the fraction by that number.
- Count the number of zeros in the denominator and place the decimal from the right hand of the numerator and then remove the denominator.
- Insert 0 at the left of the numerator if it has fewer digits.

Example:

Convert the fraction

Solution:

Step 1: We know that 5 Ă— 2 = 10. Therefore, multiply the numerator and the denominator of the given fraction by 2.

Step 2: The denominator has 1 zero. Place a decimal point after one digit.

Therefore,

Long Division Method

- Divide the numerator by the denominator.
- Put a decimal point in the quotient directly above the decimal point in the dividend.
- Add 0 in the dividend if required to complete the division.

Example:

Convert the fraction

Solution:

- Consider 3 as the dividend and 4 as the divisor.
- Since 4 > 3. Put 0 above 3 in the quotient and then place a decimal point.
- Add 0 after 3. Now consider the number as 30.
- We know 4 Ă— 7 = 28. Write 28 below 30 and 7 in the quotient.
- Subtract 28 from 30 to get 2.
- Put 0 after 2 and consider the number as 20.
- We know 4 Ă— 5 = 20. Write 20 below 20 and 5 in the quotient.
- Subtract 20 from 20 to get 0.

Therefore,

Method to convert decimals to fractions

- Observe the number of digits after the decimal point.
- The denominator of the fraction will be in the power of 10. The number of zeros will be the same as the number of digits after the decimal point.
- The numerator of the fraction will be the numbers in decimal.

Example:

Convert the decimal 0.04 to the fraction.

Solution:

The given decimal has 2 digits after the decimal point. Therefore, the denominator of the equivalent fraction will be 100.

The numerator will be 4.

Therefore, the equivalent fraction is