Dividing Decimals Formula

The Formula

\frac{a}{b} = \frac{a \times 10^n}{b \times 10^n} where 10^n makes b a whole number

When to use: If you want to split \7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is 0.4, multiply both numbers by 10 to get 72 \div 4 = 18$. You haven't changed the answer—just made it easier to compute.

Quick Example

7.2 \div 0.4 = 72 \div 4 = 18 \text{(multiply both by 10 to eliminate the decimal in the divisor)}

Notation

Move the decimal point in both divisor and dividend the same number of places to the right until the divisor is a whole number

What This Formula Means

Dividing numbers that contain decimal points, typically by converting the divisor to a whole number (multiplying both divisor and dividend by a power of 10) and then performing long division.

If you want to split \7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is 0.4, multiply both numbers by 10 to get 72 \div 4 = 18$. You haven't changed the answer—just made it easier to compute.

Worked Examples

Example 1

easy
Calculate \(3.6 \div 4\).

Solution

  1. 1
    Think: \(36 \div 4 = 9\).
  2. 2
    Since \(3.6 = 36 \times 0.1\), we get \(3.6 \div 4 = 0.9\).
  3. 3
    Or: \(4 \times 0.9 = 3.6\) ✓.

Answer

0.9
Divide as whole numbers (\(36 \div 4 = 9\)), then adjust the decimal: \(3.6 \div 4 = 0.9\).

Example 2

medium
Calculate \(5.4 \div 0.6\).

Common Mistakes

  • Moving the decimal in the divisor but forgetting to move it in the dividend
  • Misplacing the decimal point in the quotient during long division
  • Stopping the division too early instead of continuing with zeros to get a more precise answer

Why This Formula Matters

Dividing decimals is needed for unit rates (price per ounce), averages, and converting between measurement units.

Frequently Asked Questions

What is the Dividing Decimals formula?

Dividing numbers that contain decimal points, typically by converting the divisor to a whole number (multiplying both divisor and dividend by a power of 10) and then performing long division.

How do you use the Dividing Decimals formula?

If you want to split \7.20 equally among 3 people, you're dividing a decimal. The trick for harder problems is: if the divisor is 0.4, multiply both numbers by 10 to get 72 \div 4 = 18$. You haven't changed the answer—just made it easier to compute.

What do the symbols mean in the Dividing Decimals formula?

Move the decimal point in both divisor and dividend the same number of places to the right until the divisor is a whole number

Why is the Dividing Decimals formula important in Math?

Dividing decimals is needed for unit rates (price per ounce), averages, and converting between measurement units.

What do students get wrong about Dividing Decimals?

Remembering to move the decimal in both the divisor AND the dividend by the same number of places.

What should I learn before the Dividing Decimals formula?

Before studying the Dividing Decimals formula, you should understand: division, long division, place value.