How to Multiply and Divide Decimals? (+FREE Worksheet!)

Multiplying and dividing decimals are skills you will use throughout the GED Math test — in money problems, measurement conversions, and data questions. Once you learn two straightforward rules (where to place the decimal point), these problems become as easy as whole-number arithmetic. This guide walks you through each rule with clear examples and practice exercises.

What Are Decimals?

A decimal is a way of writing numbers that are between whole numbers. The decimal point separates the whole-number part from the fractional part. For example, \(\color{blue}{3.75}\) means 3 wholes and 75 hundredths. Every decimal can also be written as a fraction: \(\color{blue}{3.75 = \frac{375}{100} = \frac{15}{4}}\).

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How to Multiply Decimals

Multiplying decimals follows the same steps as multiplying whole numbers, with one extra step at the end for the decimal point.

Step 1: Multiply as if the numbers are whole numbers

Ignore the decimal points completely and multiply the digits.

Step 2: Count total decimal places

Count the total number of digits to the right of the decimal point in both factors combined.

Step 3: Place the decimal point

Starting from the right of the product, count left by that total number of places and insert the decimal point.

Quick example: \(\color{blue}{2.3 \times 1.4}\)

Multiply \(\color{blue}{23 \times 14 = 322}\). Total decimal places: \(\color{blue}{1 + 1 = 2}\). So the answer is \(\color{blue}{3.22}\).

How to Divide Decimals

Division with decimals uses one key strategy: make the divisor a whole number before you divide.

Step 1: Move the decimal in the divisor

Shift the decimal point in the divisor to the right until it becomes a whole number. Count how many places you moved it.

Step 2: Move the decimal in the dividend the same number of places

Shift the dividend’s decimal point the same number of places to the right (add zeros if needed).

Step 3: Divide normally

Now divide as you would with whole numbers and bring the decimal straight up into the quotient.

Quick example: \(\color{blue}{6.4 \div 0.8}\)

Move each decimal one place right: \(\color{blue}{64 \div 8 = 8}\). Answer: \(\color{blue}{8}\).

Step-by-Step Summary

1. To multiply: Multiply as whole numbers, then count the total decimal places in both factors and place the decimal point that many spots from the right.
2. To divide: Move the divisor’s decimal point right until it is a whole number; move the dividend’s decimal point the same number of places; then divide normally.
3. Always double-check reasonableness: multiplying two numbers less than 1 gives a smaller result; dividing by a decimal less than 1 gives a larger result.

Watch: Multiplying and Dividing Decimals (Video Lesson)

This Math Antics lesson covers decimal arithmetic including multiplication and division with visual step-by-step examples:

Worked Examples

Example 1: Find \(\color{blue}{4.5 \times 0.3}\)

Multiply \(\color{blue}{45 \times 3 = 135}\). Total decimal places: \(\color{blue}{1 + 1 = 2}\). Place decimal 2 from the right: \(\color{blue}{1.35}\).

Example 2: Find \(\color{blue}{0.6 \times 0.04}\)

Multiply \(\color{blue}{6 \times 4 = 24}\). Total decimal places: \(\color{blue}{1 + 2 = 3}\). Result is \(\color{blue}{0.024}\) (need a leading zero to have 3 decimal places).

Example 3: Find \(\color{blue}{8.4 \div 0.07}\)

Move the divisor decimal 2 places right: \(\color{blue}{0.07 \rightarrow 7}\). Move dividend 2 places right: \(\color{blue}{8.4 \rightarrow 840}\). Divide: \(\color{blue}{840 \div 7 = 120}\).

Example 4: Find \(\color{blue}{12.6 \div 1.4}\)

Move each decimal 1 place right: \(\color{blue}{126 \div 14 = 9}\). Answer: \(\color{blue}{9}\).

More Practice: Khan Academy Video

This Khan Academy video introduces multiplying decimals with clear visual models:

Exercises

1. \(\color{blue}{3.6 \times 0.5}\)
2. \(\color{blue}{0.8 \times 0.09}\)
3. \(\color{blue}{7.2 \times 1.5}\)
4. \(\color{blue}{9.6 \div 0.4}\)
5. \(\color{blue}{5.25 \div 0.05}\)
6. \(\color{blue}{14.4 \div 1.2}\)

Answers

1. \(\color{blue}{1.80}\)
2. \(\color{blue}{0.072}\)
3. \(\color{blue}{10.80}\)
4. \(\color{blue}{24}\)
5. \(\color{blue}{105}\)
6. \(\color{blue}{12}\)

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Frequently Asked Questions

Why do you count decimal places when multiplying?

Because multiplying by 10, 100, etc. shifts the decimal point. Counting total decimal places is a shortcut that accounts for those shifts automatically, keeping the answer correctly scaled.

Does dividing by a decimal always give a bigger answer?

When the divisor is between 0 and 1 (exclusive), yes — the quotient is larger than the dividend. For example, \(\color{blue}{5 \div 0.5 = 10}\). When the divisor is greater than 1, the quotient is smaller.

What if the product doesn’t have enough digits to place the decimal?

Add leading zeros. For instance, \(\color{blue}{0.2 \times 0.3 = 0.06}\) — the product of 2 and 3 is 6, and since we need 2 decimal places, we write \(\color{blue}{0.06}\).

Related Topics

• Adding and Subtracting Decimals
• Convert Between Fractions and Decimals
• Order of Decimals, Mixed Numbers, and Fractions
• Repeating Decimals
• Using Number Lines to Represent Rational Numbers