## Decimal fraction

Decimal fraction is a fraction whose denominator is exponents of 10.

Example: 3/10, 27/100, 305/1000 are fractions in decimal

We can write the decimal number system for these fractions as follows.

3/10 since this fraction's denominator is 10 that power of 10 is 1.

So we can write this as 0.3 as we have the power of 10 as 1, we will have only one digit after the decimal point.

Example:Convert the following numbers as decimals.

1. 3 and 25/10000
2. 67/1000
3. 458 and 2/100

1)Solution:

•  Here we have mixed number.
• The denominator is 10000 which is 10 raised to the power of 4. So we must have 4 digits after the decimal point.
• But here we have only two digits (that is only 25) in the numerator. So we must add two more zeros' after the decimal point. (That is before 25).
• So the answer is 3.0025

2)Solution:

• Since it is not a mixed number, we do not have any digits before the decimal point. So we can put '0' in front of the decimal point.
• Here we have 1000 in the denominator which 10 raised to the power of 3. So we must have 3 digits after the decimal point.
• But we have only two digits in the numerator. So we must add one zero after the decimal point(before 67).
• So the answer is 0.067

3)Solution:

• The given number is a mixed number. So the whole number 458 will come before the decimal point.
• Here we have 100 in the denominator, which is square of 10. So we must have 2 digits after the decimal point.
• But we have only one digit in the numerator. So we must add one '0' after the decimal point (before 20.
• So the answer is 458.02.

Example:Convert the following decimals into fractions.

1. 0.8
2. 45.003

Solution:

1. Since we have only one digit after the point, the denominator of the fraction should be only 10. So the answer is 8/10
2. We have two digits before the decimal the fraction is a mixed number. so the answer is 45 and 3/1000.

Practice problems:

Convert the following decimal numbers into their corresponding fractions:

• 32.007
• 0.0003

Convert the following fractions into decimal numbers.

• 86 and 27/1000
• 98/100