Lesson 13: Divide by Decimals

Property

To divide a whole number by a decimal, convert the divisor into a whole number by multiplying both the divisor and the dividend by the same power of 10. This is equivalent to moving the decimal point in both numbers to the right by the same number of places. Then, perform the division as you would with whole numbers.

Examples

• To solve $42 \div 0.7$, multiply both numbers by 10:

• To solve $15 \div 0.03$, multiply both numbers by 100:

Explanation

When dividing a whole number by a decimal, the key is to transform the problem into one you already know how to solve: division by a whole number. You can do this by multiplying both the dividend (the number being divided) and the divisor (the number you are dividing by) by the same power of 10 (like 10, 100, or 1000). This process effectively moves the decimal point in both numbers to the right, creating an equivalent division problem with a whole number divisor. After setting up the equivalent problem, you can use long division to find the final answer.