Long Division with Decimals — Definition, Formula & Examples
Long division with decimals is the process of dividing numbers that contain decimal points using the standard long division method. You handle the decimal by shifting it in the divisor and dividend before dividing, or by placing it directly above its position in the dividend.
When the divisor or dividend (or both) contain decimal values, the division is performed by first converting the divisor to a whole number — multiplying both divisor and dividend by the appropriate power of 10 — then executing the standard long division algorithm, placing the decimal point in the quotient directly above its new position in the adjusted dividend.
How It Works
If the divisor has a decimal, move the decimal point to the right until the divisor becomes a whole number. Move the decimal in the dividend the same number of places to the right, adding zeros if needed. Place the decimal point in the quotient directly above its position in the adjusted dividend. Then divide as you normally would with whole numbers, bringing down digits one at a time. If there is a remainder, add zeros after the decimal in the dividend and continue dividing until the answer terminates or you reach the desired precision.
Worked Example
Problem: Divide 9.36 ÷ 0.4
Step 1: Make the divisor a whole number. Multiply both 0.4 and 9.36 by 10.
Step 2: Set up the long division: 93.6 ÷ 4. Place the decimal in the quotient above the decimal in 93.6. Then divide: 4 goes into 9 twice (8), remainder 1. Bring down 3 to get 13. 4 goes into 13 three times (12), remainder 1. Bring down 6 to get 16. 4 goes into 16 exactly 4 times.
Step 3: Check by multiplying the quotient by the original divisor.
Answer: 9.36 ÷ 0.4 = 23.4
Why It Matters
Dividing decimals comes up whenever you split money, calculate unit prices, or convert measurements. Mastering this skill builds the foundation for working with fractions, ratios, and algebra in middle school.
Common Mistakes
Mistake: Moving the decimal in the divisor but forgetting to move it the same number of places in the dividend.
Correction: Always move the decimal the same number of places in both the divisor and the dividend. This keeps the value of the division unchanged because you are multiplying both numbers by the same power of 10.