Decimals and Fractions

Proper Fraction is a fraction in which the numerator is less than the denominator

To write a proper fraction into a decimal whose denominator is 10 or a power of 10:

1) Count the number of zeros in the denominator of the fraction.

2) Insert a decimal point in the numerator after moving from the right to the left by as many digits as there are zeros in the denominator.

For example: 3/100 = 0.03, as there are two zeros in the denominator of 3/100

To write a proper fraction as a decimal:

1) Divide the numerator by the denominator.

2) For that, place a decimal point at the end of the numerator and corresponding to this zero we will place a decimal point in the quotient also.

3) Extend the numerator by adding zeros after the decimal point such that it becomes divisible by the denominator

Improper Fraction is a fraction in which the numerator is greater than the denominator

A mixed number is the sum of a whole number and a proper fraction.
For e.g.: In 5 2/3, 5 is a whole number and 2/3 is a proper fraction

Improper fraction is the fraction form of a mixed number

To write an improper fraction having denominator 10 or a power of 10 into a decimal:
1) Count the number of zeros in the denominator of the fraction
2) Insert a decimal point in the number moving from the right to the left by as many digits as there are zeros in the denominator
For example: 35/10 = 3.5, as there is one zero in the denominator of 35/10

To write a mixed number as a decimal:
1) Divide the numerator of the fraction part by its denominator.
2) For that, place a decimal point at the end of the numerator.
And then extend the numerator by adding zeros after the decimal point such that it becomes divisible by the denominator.
3) For a mixed number, decimal equivalent = Whole number part + Decimal equivalent of fraction part

To write an improper fraction as a decimal:
1) Divide the numerator by the denominator.
2) If the numerator is not divisible by the denominator then place a decimal point at the end of the numerator and corresponding to this zero we will place a decimal point in the quotient also.
3) Extend the numerator by adding zeros after the decimal point such that it becomes divisible by the denominator

To write a decimal (less than 1) as a fraction follow the steps listed below:
Step 1: Write the given decimal without the decimal point as the numerator of the fraction
Step 2: In the denominator, write 1 followed by as many zeros as there are digits after the decimal point

For example: Fraction equivalent of 0.8 = 8/10 = 4/5

To write a decimal (greater than 1) as a fraction follow the 3 simple steps:
Step 1: Write the decimal as the sum of its whole number part and decimal part

Fraction equivalent of decimal number = Whole number part + fraction equivalent of decimal part

Step 2: Find the fraction equivalent of decimal part
1) Write the decimal part of the given number without the decimal point as the numerator of the fraction
2) In the denominator, write 1 followed by as many zeros as there are digits after the decimal point

For example: Fraction equivalent of 4.8 = 4 + Fraction equivalent of 0.8
= 4 + 8/10
= 4 + 4/5 = 4 4/5

Fraction: A number of the form p/q, where p is a whole number and q is a natural number.
For example: 2/3

Decimal: A number that has a whole number part and a fraction part separated by a decimal point.
For example: 2.35

Like Fractions: Fractions with the same denominator are like fractions.
For example: 5/16 and 3/16 are like fractions since their denominators are same

Unlike Fractions: Fractions with different denominators are called unlike fractions.
For example: 1/2 and 3/4 are unlike fractions as their denominators are different

When two fractions have the same denominator, the one with the smaller numerator is smaller