Multiplying and Dividing Decimals

Same digits, different point — figure out where it lands.

🧱 See It

Picture a rectangle that's 1.2 units wide and 0.4 units tall. Chop the whole unit square into 100 tiny squares — a 10×10 grid — so each tiny square is worth one hundredth (0.01).

1.2 is 12 tenths across. 0.4 is 4 tenths down. That's 12 × 4 = 48 tiny squares, and each tiny square is 0.01 — so the shaded rectangle is worth 48 hundredths, or 0.48.

✏️ Draw It

You don't need to draw 48 tiny squares every time. There's a shortcut: ignore the decimal points, multiply like whole numbers, then put the point back afterward.

  1. Cover up both decimal points and multiply as if they were whole numbers: 12 × 4 = 48
  2. Count the total number of digits after the decimal point in the original numbers: 1.2 has 1, 0.4 has 1 — total 2.
  3. Starting from the right of your answer, count that many places over and drop in the point: 48 → 0.48
The point always lands based on the TOTAL decimal places in both numbers you started with — not on anything in the answer itself.

🔢 Write It

Multiplying:

1.2 × 0.4

Multiply as whole numbers: 12 × 4 = 48

Total decimal places: 1 + 1 = 2

1.2 × 0.4 = 0.48

Dividing:

6.4 ÷ 0.8

Multiply both numbers by 10 to clear the decimal in the divisor:

64 ÷ 8

6.4 ÷ 0.8 = 8

Dividing lets you shift BOTH decimal points the same number of spots — it doesn't change the answer, it just clears the mess.

💡 Worked Examples

Example 1 — Multiplication: 2.5 × 1.3

  1. Ignore the points, multiply as whole numbers: 25 × 13 = 325
  2. Count total decimal places: 2.5 has 1, 1.3 has 1 — total 2.
  3. Count 2 places from the right of 325: 3.25
  4. Answer: 2.5 × 1.3 = 3.25

Example 2 — Division: 4.5 ÷ 0.5

  1. The divisor 0.5 has 1 decimal place, so shift both points 1 spot to the right.
  2. 4.5 ÷ 0.5 becomes 45 ÷ 5
  3. Divide the whole numbers: 45 ÷ 5 = 9
  4. Answer: 4.5 ÷ 0.5 = 9

🧠 Quick Reference

Multiplying: count the total decimal places in BOTH numbers, then place the point that many spots from the right in your answer.
Dividing: shift the decimal point in the divisor until it's a whole number, then shift the dividend's point the exact same number of spots.
👪 For Parents & Tutors

BC Curriculum (Level 1 / Grade 6, Number): "Multiplication and division of decimals."

Why estimation-first matters: Before working out the precise answer, round both numbers to whole numbers and multiply or divide those instead. For 2.5 × 1.3, rounding gives roughly 3 × 1 = 3, so the precise answer should land near 3 — 3.25 checks out, but 32.5 or 0.325 would immediately look wrong. This sanity check catches decimal-point placement errors without needing to redo the whole calculation.

Watch for: The working-memory trap here isn't the multiplication or division itself — it's losing count of how many decimal places to shift, or forgetting to shift the divisor's point at all partway through a division problem. Encourage him to always estimate first, do the precise calculation second, then compare the two. If they don't roughly match, the decimal point is probably in the wrong place.

Comes up again: This resurfaces at Level 2 (Grade 7) once negative numbers enter the picture — integer and decimal operations combined — and continues to matter anywhere decimals appear in later ratio, percent, and algebra work.