Multiplying and Dividing Decimals

What You Will Learn

• Multiply decimals by 10, 100 and 1,000.
• Multiply decimal numbers by whole numbers.
• Multiply two decimal numbers.
• Divide decimals by whole numbers.
• Use estimation to check answers and solve practical problems.

1. Multiply by 10, 100 and 1,000

In the base-ten place-value system, multiplying by 10 makes a number ten times as large. Each digit moves one place to the left in the place-value chart. Multiplying by 100 moves digits two places to the left; multiplying by 1,000 moves them three places.

2. Multiply a Decimal by a Whole Number

Multiply as you would with whole numbers, then place the decimal point so the answer has the correct value. Estimate first to help you check.

Worked example: 2.4 × 3

1. Think of 2.4 as 24 tenths.
2. Multiply 24 × 3 = 72.
3. 72 tenths = 7.2.

Answer: 7.2.

Another example: 1.25 × 4

125 hundredths × 4 = 500 hundredths = 5.00 = 5.

3. Multiply Two Decimals

First multiply the numbers as if the decimal points were not there. Then count the total number of decimal places in both factors and place that many decimal digits in the product.

Worked example: 1.2 × 0.3

1. Ignore the decimal points for a moment: 12 × 3 = 36.
2. There is one decimal place in 1.2 and one in 0.3, so the product needs two decimal places.
3. Write 36 as 0.36.

Answer: 0.36.

Another example: 2.5 × 1.4

25 × 14 = 350. There are two decimal places altogether, so the answer is 3.50 = 3.5.

4. Divide a Decimal by 10 or 100

Dividing by 10 makes a number ten times smaller. Each digit moves one place to the right in the place-value chart. Dividing by 100 moves digits two places to the right.

• 48 ÷ 10 = 4.8
• 4.8 ÷ 10 = 0.48
• 48 ÷ 100 = 0.48
• 7.5 ÷ 100 = 0.075

5. Divide a Decimal by a Whole Number

Divide as usual, keeping the decimal point in the quotient directly above the decimal point in the number being divided.

Worked example: 8.4 ÷ 4

1. Think of 8.4 as 84 tenths.
2. 84 tenths ÷ 4 = 21 tenths.
3. 21 tenths = 2.1.

Answer: 2.1.

Another example: 6.75 ÷ 3

675 hundredths ÷ 3 = 225 hundredths = 2.25.

6. Check with Estimation

Estimate before calculating. If you multiply two positive numbers and both are less than one, the product will be smaller than either factor. If you divide a positive number by a number greater than one, the result will be smaller than the starting number.

7. Solve Everyday Problems

Example 1: Price of several items

One notebook costs $1.25. What is the cost of 4 notebooks?

$1.25 × 4 = $5.00.

Example 2: Sharing a distance

A 7.5-kilometre walk is shared equally over 3 days. How far is walked each day?

7.5 ÷ 3 = 2.5 kilometres.

Example 3: Area

A rectangle is 2.4 metres long and 1.5 metres wide. Find its area.

2.4 × 1.5 = 3.6 square metres.

8. Common Mistakes to Avoid

9. Practice Exercises

Try these before revealing the answers.

1. 3.7 × 10
2. 0.56 × 100
3. 2.3 × 4
4. 1.5 × 0.4
5. 9.6 ÷ 10
6. 7.2 ÷ 3
7. Explain why 8.4 ÷ 0 is undefined.
8. A 2.5-metre board is cut into 5 equal pieces. How long is each piece?

10. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

12. Lesson Summary

• Multiplying by 10, 100 or 1,000 makes a number larger by shifting digits to higher place values.
• When multiplying decimals, count the decimal places in both factors.
• When dividing decimals by whole numbers, place the decimal point correctly in the quotient.
• Use zeros as placeholders when needed.
• Estimate to check that the answer is reasonable.