Lesson 6: Dividing Decimals by Decimals

Property

When dividing numbers with the same decimal unit, you can divide them as if they were whole numbers.

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.