Dividing Decimals — Definition, Formula & Examples
Dividing decimals is the process of dividing numbers that contain a decimal point. You simplify the problem by shifting the decimal point in both the divisor and dividend until the divisor becomes a whole number, then divide as usual.
To divide one decimal by another, multiply both the dividend and the divisor by the same power of 10 so that the divisor is an integer. Then perform standard long division, placing the decimal point in the quotient directly above its position in the adjusted dividend.
Key Formula
Where:
- = The dividend (the number being divided)
- = The divisor (the number you divide by)
- = The number of decimal places in the divisor
How It Works
The key idea is that multiplying both numbers by the same power of 10 does not change the result of the division — it just removes the decimal from the divisor. Count how many decimal places are in the divisor, then move the decimal point that many places to the right in both the divisor and the dividend. If the dividend runs out of digits, add zeros. Once the divisor is a whole number, perform long division and bring the decimal point straight up into your answer.
Worked Example
Problem: Divide 7.56 ÷ 0.6
Step 1: Count the decimal places in the divisor. The divisor 0.6 has 1 decimal place, so multiply both numbers by 10.
Step 2: Rewrite the problem with the new numbers.
Step 3: Divide using long division. 6 goes into 75 twelve times (6 × 12 = 72) with a remainder of 3. Bring down the 6 to get 36. 6 goes into 36 exactly 6 times.
Answer: 7.56 ÷ 0.6 = 12.6
Another Example
Problem: Divide 4.5 ÷ 0.25
Step 1: The divisor 0.25 has 2 decimal places, so multiply both numbers by 100.
Step 2: Rewrite the problem.
Step 3: Divide: 25 goes into 450 exactly 18 times because 25 × 18 = 450.
Answer: 4.5 ÷ 0.25 = 18
Why It Matters
Dividing decimals comes up constantly in real life — splitting a restaurant bill, calculating unit prices at the grocery store, or converting measurements. It is a foundational skill in 6th- and 7th-grade math that you will rely on in algebra, chemistry, and any field that uses data and measurements.
Common Mistakes
Mistake: Moving the decimal in the divisor but forgetting to move it the same number of places in the dividend.
Correction: Always shift the decimal the same number of places in both numbers. If you multiply the divisor by 100, you must also multiply the dividend by 100.
Mistake: Placing the decimal point in the wrong spot in the quotient.
Correction: After adjusting both numbers, place the decimal point in the quotient directly above where it sits in the adjusted dividend before you start dividing.