Lesson 14: Divide Decimals

Property

To divide a decimal by a whole number, use long division. Place the decimal point in the quotient directly above the decimal point in the dividend. Then, divide as you would with whole numbers.

Examples

• $6.8 \div 2 = 3.4$
• $7.5 \div 5 = 1.5$
• $1.89 \div 9 = 0.21$

Explanation

Dividing a decimal by a whole number is very similar to regular long division. The most important step is to place the decimal point in your answer (the quotient) directly above the decimal point in the number being divided (the dividend). After that, you can ignore the decimal and divide as you normally would, from left to right. This process effectively splits the decimal amount into a specific number of equal groups.

Property

To divide a decimal by a decimal, multiply both the dividend and the divisor by the same power of 10 to make the divisor a whole number. This creates an equivalent problem.

For example, $1.25 \div 0.5$ is equivalent to $12.5 \div 5$.

Examples

• $4.8 \div 0.6 = (4.8 \times 10) \div (0.6 \times 10) = 48 \div 6 = 8$
• $7.2 \div 0.09 = (7.2 \times 100) \div (0.09 \times 100) = 720 \div 9 = 80$
• $1.32 \div 0.4 = (1.32 \times 10) \div (0.4 \times 10) = 13.2 \div 4 = 3.3$

Explanation

When dividing by a decimal, the goal is to convert the problem into one you already know how to solve: dividing by a whole number. You can do this by moving the decimal point in both the divisor and the dividend the same number of places to the right. This is the same as multiplying both numbers by a power of 10, like 10, 100, or 1000. Once the divisor is a whole number, you can perform the division as you normally would.