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

How to multiply and divide decimals, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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: \(\color{blue}{3.75 = \frac{375}{100} = \frac{15}{4}}\).

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

What is the rule for multiplying and dividing decimals?

To multiply, ignore the decimal points, multiply as whole numbers, then give the answer as many decimal places as both factors have in total. For 0.6 × 0.07, multiply 6 × 7 = 42 and count three decimal places to get 0.042. To divide, move the decimal point in the divisor to make it a whole number and move the dividend’s decimal point the same number of places.

How do you multiply and divide decimals by powers of 10?

Move the decimal point one place for each zero. Multiplying by 10, 100 or 1,000 moves it right 1, 2 or 3 places, so 4.56 × 100 = 456. Dividing moves it left, so 3.2 ÷ 1,000 = 0.0032. Add zeros as placeholders when you run out of digits, and the size of the answer will always make sense.

How do you multiply and divide decimals with whole numbers?

Multiply as usual and keep the decimal places from the decimal factor: 0.75 × 8 = 6.00, or simply 6. When dividing a decimal by a whole number, place the decimal point in the quotient directly above the one in the dividend and divide normally, so 9.6 ÷ 4 = 2.4. This comes up often in money problems, like splitting a bill.

How do you divide decimals without a calculator?

Make the divisor a whole number first. For 7.5 ÷ 0.25, move both decimal points two places right to get 750 ÷ 25, which equals 30. This works because multiplying both numbers by 100 does not change the quotient. Then use long division, and estimate first (7.5 is about 7, and 7 ÷ 0.25 is 28) to check your answer.

What grade is multiplying and dividing decimals?

Under the Common Core standards, students start multiplying and dividing decimals to hundredths in 5th grade, then build fluency with multi-digit decimals in 6th grade. Adults review the same skills for tests such as the GED Math test, where decimals appear in money, measurement and data questions. Grade expectations can vary a little by state.

How do you multiply and divide negative and positive decimals?

Work out the decimal answer first, then use the integer sign rules. If the signs are different, the answer is negative: −1.5 × 0.4 = −0.6. If the signs are the same, the answer is positive: −2.4 ÷ −0.6 = 4. Placing the decimal point and choosing the sign are separate steps, so handle them one at a time.

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