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Mathematics › 🌉 Grade 5 › Multiplying Decimals: Finding Where the Point Lands
🌉 Grade 5 · Lesson 9 of 11

Multiplying Decimals: Finding Where the Point Lands

Multiply as if the dots don't exist — then count to put the point in its home.

Grade 5Elementary
Multiplying Decimals: Finding Where the Point Lands — illustration
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The big idea: Multiplying decimals follows the exact same steps as whole-number multiplication. The only extra task is placing the decimal point correctly at the end: count the total decimal places in both factors and put that many decimal places in the product. No alignment is needed before multiplying — the counting rule handles everything.
🎯 By the end, you'll be able to
  • Multiply decimals by first ignoring, then restoring, the decimal point
  • Count total decimal places in both factors to place the point in the product
  • Explain why multiplying two numbers less than 1 produces a smaller number
  • Use a 10×10 grid to visualize decimal products as parts of one whole
📎 You should already know
  • Decimal place value (tenths and hundredths)
  • Multi-digit whole-number multiplication

The disappearing decimal puzzle

A student is asked to find 0.3 × 0.4. She thinks: “3 × 4 = 12, so the answer must be 1.2.” But the correct answer is 0.12. Where did the extra decimal place come from?

To understand it, picture a 10 × 10 grid where the entire grid equals 1 whole (100 small squares). Shade 3 of the 10 columns to show 0.3. Shade 4 of the 10 rows to show 0.4. The overlap — the patch shaded in both directions — is 3 × 4 = 12 squares out of 100, which equals 0.12. That’s the product, and it is smaller than either factor!

Reading the 10×10 grid

The grid makes the decimal-place rule visible:

  • 0.3 means 3 out of 10 columns — each column is one-tenth of the grid.
  • 0.4 means 4 out of 10 rows — each row is also one-tenth of the grid.
  • The overlap is 3/10 × 4/10 = 12/100 = 0.12.

Notice: 0.3 has 1 decimal place, 0.4 has 1 decimal place, and the product 0.12 has 2 decimal places — exactly 1 + 1. That is the counting rule in action.

🎮 Decimal Multiplication Grid LIVE
The shaded columns show the first factor and the shaded rows show the second. The darker overlap region is the product. A decimal-place counter shows how many places land in the answer.
🔑 The three-step decimal-multiplication rule
  1. Ignore the decimal points and multiply as whole numbers.
  2. Count decimal places: add up all the decimal places in both factors.
  3. Place the point: count that many places from the right edge of the whole-number product and insert the decimal point there.

Example — 0.3 × 0.4: 3 × 4 = 12; decimal places: 1 + 1 = 2; count 2 from the right of 12 → 0.12.

⚠️ Multiplying two numbers under 1 gives a SMALLER number — that's correct!

Many students expect multiplying to always make numbers bigger. With whole numbers greater than 1, that is true. But 0.3 × 0.4 = 0.12, which is smaller than both 0.3 and 0.4.

Think of it this way: you are taking 0.3 of a group that is already only 0.4 — a fraction of something already small must be even smaller. The decimal-counting rule automatically produces this correct, smaller number. Trust the count!

📝 Worked example: Find 2.3 × 0.6.
  1. Count decimal places: 2.3 has 1, 0.6 has 1. Total = 2 decimal places needed in the product.
  2. Ignore decimal points and multiply: 23 × 6 = 138.
  3. Place the decimal point 2 places from the right of 138: 1.38.
  4. Check: 2.3 is a bit more than 2, and 0.6 is a bit more than one-half, so the answer should be a little over 1. → 1.38 is reasonable.
✓ 2.3 × 0.6 = <strong>1.38</strong>.
📝 Worked example: Find 0.04 × 5.
  1. Count decimal places: 0.04 has 2, 5 has 0. Total = 2 decimal places.
  2. Multiply as whole numbers: 4 × 5 = 20.
  3. Place the decimal 2 places from the right of 20: 0.20.
  4. Simplify: 0.20 = 0.2 (the trailing zero can be dropped).
  5. Check: 0.04 is 4 hundredths; 5 groups of 4 hundredths = 20 hundredths = 0.20. Correct!
✓ 0.04 × 5 = <strong>0.2</strong>.
\[ \text{decimal places in product} = \text{d.p. in factor}_1 + \text{d.p. in factor}_2 \]
Count the decimal places in each factor, add them, and that total is exactly how many decimal places the product must have.

Check your understanding

1. What is 0.5 × 0.5?
5 × 5 = 25. Decimal places: 1 + 1 = 2. Count 2 from the right of 25 → 0.25.
2. What is 1.2 × 3?
12 × 3 = 36. Decimal places: 1 + 0 = 1. Place 1 from the right → 3.6.
3. What is 0.04 × 7?
4 × 7 = 28. Decimal places: 2 + 0 = 2. Place 2 from the right → 0.28.
4. A rectangular garden is 0.6 m wide and 0.9 m long. What is its area?
6 × 9 = 54. Decimal places: 1 + 1 = 2. Answer: 0.54 m². The garden is less than 1 m on each side, so the area must be less than 1 m².
5. A student multiplied 1.5 × 0.4 and wrote 60 as the answer. What went wrong?
15 × 4 = 60 is the whole-number product, but 1.5 has 1 decimal place and 0.4 has 1 decimal place — total 2. Place 2 from the right of 60: the correct answer is 0.60 = 0.6.
✅ Key takeaways
  • Multiply decimals exactly like whole numbers — ignore the decimal points during multiplication.
  • Count the total decimal places in both factors; that is how many the product must have.
  • Count from the right of the whole-number product and insert the decimal point there.
  • Multiplying two numbers less than 1 always gives a product smaller than either factor — this is expected and correct.
  • A 10×10 grid models decimal multiplication visually: shaded columns × shaded rows = overlap squares out of 100.
  • Always sanity-check: is the product a reasonable size given the size of the factors?