Multiplying decimals to thousandths and the metric system
الأسبوع 10 · ضرب الكسور العشرية حتى الأجزاء من ألف والنظام المتري · 3 دروس
2
Hundredths and thousandths in the algorithm
Discover Mathematics P5: Term 1, Unit 5, Lessons 5–10
GoalMultiply decimals with hundredths and thousandths by counting the decimal places.
New words
decimal places · the number of digits after the decimal pointplace holder zero · a zero written after the point to hold a place, as in 0.0042
Explanation
The standard algorithm works for any decimals. Step 1: ignore the decimal points and multiply as whole numbers. Step 2: count all the decimal places in the two factors. Step 3: put the decimal point in the product so that it has that many places, adding zeros in front when needed. For 3.46 × 2.5: 346 × 25 = 8,650. The factors have 2 + 1 = 3 decimal places, so the product is 8.650 = 8.65. For 0.06 × 0.07: 6 × 7 = 42, and 2 + 2 = 4 places, so we write 0.0042, using two zeros as place holders. Estimate to check: 3.46 × 2.5 is close to 3.5 × 2.5 = 8.75.
Factors
Whole numbers
Places
Product
3.46 × 2.5
346 × 25 = 8,650
3
8.65
4.07 × 3.2
407 × 32 = 13,024
3
13.024
0.06 × 0.07
6 × 7 = 42
4
0.0042
Worked examples
Work out 3.46 × 2.5. 346 × 25 = 346 × 20 + 346 × 5 = 6,920 + 1,730 = 8,650. The factors have 2 and 1 decimal places, 3 in all, so the product is 8.650, which is 8.65. Estimate: 3.5 × 2.5 = 8.75, close to 8.65.
Work out 4.07 × 3.2. 407 × 32 = 407 × 30 + 407 × 2 = 12,210 + 814 = 13,024. There are 2 + 1 = 3 decimal places, so the product is 13.024. Estimate: 4 × 3 = 12, close to 13.024.
Work out 0.06 × 0.07 and 0.125 × 0.4. First, 6 × 7 = 42 and 4 decimal places, so 0.0042 (two zeros are written after the point to keep the places). Second, 125 × 4 = 500 and 4 decimal places, so 0.0500, which is 0.05.
Class activity
Place the point. Write the whole-number products 288, 450 and 1,260 on cards. Then write decimal factors on other cards, such as 0.9 × 3.2, 1.8 × 2.5 and 0.12 × 10.5. Match each pair of factors with the right product and say where the decimal point goes in it.
