Grade by Grade
B. Number · Operations: Exponents, Factors, Fractions, Decimals, Integers, Percents and Proportions

Multiplying Decimals by Decimals

B2.9 A1About 45 minutes
Learning goals
  • I can use a hundredths grid to show multiplying tenths by tenths.
  • I can multiply decimals by decimals and place the decimal point correctly.
  • I can estimate to check that my product makes sense.
  • I can solve problems with money, measurement and unit prices.

Words to know

decimal place
A position to the right of the decimal point: tenths, hundredths, thousandths...
estimate
A close answer found with friendly numbers, used to check a calculation.
factor
A number being multiplied. In 2.4 × 1.5, the factors are 2.4 and 1.5.
unit price
The price for one unit, such as dollars per kilogram.

Remember from Grade 6

In Grade 6 you multiplied whole numbers by decimal tenths, like 324 × 0.7, by multiplying 324 × 7 and dividing by 10. You also learned that multiplying by a number less than 1 gives a smaller answer. Now both numbers can be decimals.

Let's start with a seed tray

A small seed tray is 0.6 m long and 0.4 m wide. What is its area?

Area = 0.6 × 0.4. Think of a 1 m by 1 m square split into a 10-by-10 grid. Each small square is 0.1 m by 0.1 m, which is one hundredth of the big square. A 0.6 by 0.4 rectangle covers 6 columns and 4 rows: 24 small squares, or 24 hundredths.

0.6 × 0.4 = 0.24 m². Tenths times tenths gives hundredths.

A black plastic seed tray full of soil and small green seedlings on a sunny windowsill.
A seed tray is a rectangle. Multiplying its decimal length by its decimal width gives its area in square metres. AI-generated image
0.60.424 hundredths= 0.24
A 10-by-10 grid is 1 whole. The shaded rectangle is 0.6 wide and 0.4 tall. It covers 6 × 4 = 24 small squares, so 0.6 × 0.4 = 0.24.

The method

  1. Estimate using friendly numbers.
  2. Multiply as if there were no decimal points.
  3. Place the decimal point. Use your estimate, or count: the product has as many decimal places as both factors together. (Tenths × tenths = hundredths; tenths × hundredths = thousandths.)

Why counting works: 0.6 × 0.4 = (6 ÷ 10) × (4 ÷ 10) = 24 ÷ 100 = 0.24.

Worked example

Example 1: Tenths by tenths

Find 2.4 × 1.5.

  1. Estimate: 2 × 1.5 = 3, or 2.5 × 1.5 is a bit less than 4. The answer is between 3 and 4.
  2. Multiply without decimals: 24 × 15 = 360.
  3. There is 1 decimal place in each factor, so 2 in the product: 3.60.
  4. 3.60 = 3.6, which matches the estimate. ✓

2.4 × 1.5 = 3.6

2 × 1 = 20.42 × 0.5 = 10.220.410.5210.4+ 0.2= 3.6
An area model for 2.4 × 1.5: split each side into a whole part and a decimal part, find the four smaller areas, and add them. 2 + 1 + 0.4 + 0.2 = 3.6.
Worked example

Example 2: Hundredths by tenths

Find 3.25 × 0.8.

  1. Estimate: 3 × 0.8 = 2.4. A bit more than 2.4.
  2. 325 × 8 = 2 600.
  3. Decimal places: 2 + 1 = 3. 2 600 → 2.600.
  4. 2.600 = 2.6. ✓

3.25 × 0.8 = 2.6

Worked example

Example 3: Unit price

Apples cost $3.40 per kilogram. You buy 2.5 kg. How much do you pay?

  1. Cost = 3.40 × 2.5.
  2. Use properties: 3.40 × 2.5 = 3.40 × 2 + 3.40 × 0.5 = 6.80 + 1.70.
  3. 6.80 + 1.70 = 8.50.

$8.50

Check with an estimate

A product of two numbers less than 1 is smaller than both: 0.4 × 0.3 = 0.12, not 1.2. If one factor is greater than 1 and the other is less than 1, the answer is between them. Always compare with your estimate before you write the final answer.

Hands-on activity

Kitchen-scale shopping

You need: a grocery flyer or receipt, a kitchen scale if you have one, a few fruits or vegetables, paper and a pencil.

  1. Find 3 items in the flyer that are priced per kilogram (for example, apples at $3.40/kg).
  2. Weigh some fruit on the scale in kilograms (to the tenth, like 1.3 kg). If you have no scale, choose masses like 0.8 kg or 1.6 kg.
  3. Estimate the cost first, then multiply the mass by the price per kilogram.
  4. Round each cost to the nearest cent.
  5. Add up your shopping total.

What to look for: an estimate first, the decimal point placed sensibly, and money rounded to 2 decimal places.

Math talk: "How did you know where the decimal point goes?"

Just for fun

Why did the decimal point get a job with a moving company?

It's an expert at moving places.

Your turn

1

0.3 × 0.2 = ?

2

0.5 × 0.8 = ?

3

1.2 × 0.4 = ?

4

2.5 × 1.6 = ?

5

3.4 × 2.1 = ?

6

0.07 × 0.6 = ?

7

4.25 × 0.4 = ?

More practice: warm-up

1

0.4 × 0.2 = ?

2

0.9 × 0.1 = ?

3

1.5 × 2 = ?

4

0.5 × 0.5 = ?

5

2.2 × 0.3 = ?

More practice: on your own

1

6.5 × 0.12 = ?

2

Cheese costs $12.50 per kilogram. How much does 1.8 kg cost?

3

A rug is 3.2 m by 2.5 m. What is its area?

4

0.25 × 0.36 = ?

5

Estimate, then calculate: 4.9 × 3.1.

Challenge

1

1.25 × 1.25 = ?

2

Mo says 0.4 × 0.3 = 1.2. Explain the mistake and give the correct answer.

3

A canoe rental costs $14.75 per hour. How much does it cost for 2.5 hours? Round to the nearest cent if needed.

Check your understanding

Quiz

1.

What is 0.7 × 0.3?

2.

What is 1.5 × 2.4?

3.

Which is the best estimate for 5.9 × 3.2?

4.

Which product is less than 0.5?

5.

Grapes cost $4.00 per kg. How much do 0.75 kg cost?

6.

How many decimal places will 2.35 × 1.4 have before you drop any zeros?

For parents and teachers

Big idea: The Ontario curriculum (B2.9) asks Grade 7 students to multiply and divide decimal numbers by decimal numbers, in various contexts. Students should understand why the decimal point goes where it does (tenths × tenths = hundredths) and use estimation as a check.

Common difficulties:

  • Lining up decimal points as in addition. That isn't needed for multiplication.
  • Misplacing the decimal point, especially when the product has zeros at the end (2.600 = 2.6) or needs extra zeros (0.07 × 0.6 = 0.042).
  • Expecting multiplication to always make bigger numbers.

How to help: Use flyers and grocery receipts with prices per kilogram. Ask, "About how much will this cost?" before calculating. This lesson builds A1 skills: estimating, reasoning about the size of an answer, and connecting math to everyday life.