6th Grade - Fraction and Decimal Conversion

Introduction

Converting numbers is required in order for the numbers to be added, subtracted, multiplied, or divided. Any operation can be easily performed if all the numbers in the expression have the same name.

For instance, $\frac{3.5}{0.5}$ or $\frac{1}{2} \div \frac{1}{3}$ compared to $3.6 \div \frac{1}{2}$ .

Fractions to Decimals

To convert a fraction to decimals divide the numerator by the denominator i.e. the numerator becomes the dividend and the denominator becomes the divisor.

Converting Decimals to Fractions

To convert decimals to a fraction:

1. Divide the number by 1.

2. Count the number of digits after the decimal point.

3. Remove the decimal point and add the same number of zeros to the denominator as the number of digits after the decimal point.

4. Reduce the fraction, if possible.

Solved Examples

Example 1: Convert $\frac{33}{2}$ to a decimal number.

Solution: Divide the numerator by the denominator. So, 33 is the dividend, and 2 is the divisor.

$33 \div 2 = 16.6$

Example 2: Convert 15.2 to a fraction.

Solution: Divide the given number by 1

$= \frac{15.2}{1}$

Count the number of digits after the decimal point (to the right of the decimal point) and put the same number of zeros in the denominator; in this case, there is 1 digit after the decimal point, so we will put 1 zero in the denominator.

$= \frac{152}{10}$

Simplify the fraction.

$\frac{152 \div 2}{10 \div 2} = \frac{76}{5}$

Example 3: Convert 27.24 to a fraction.

Solution: Divide the given number by 1

$= \frac{27.24}{1}$

Count the number of digits after the decimal point (to the right of the decimal point) and put the same number of zeros in the denominator; in this case, there are 2 digits after the decimal point, so we will put 2 zeros in the denominator.

$= \frac{2724}{100}$