A student calculates 0.6 × 0.04 by multiplying 6 × 4 = 24 and then writing 0.24 as the answer. Is this correct?
AYes — multiply the digits and keep the decimal between the two digits
BNo — the decimal point should be aligned with the factors, just like in addition
CNo — there are three total decimal places in the factors (1 + 2), so the answer should be 0.024
DYes — when both factors are less than 1, the product is always between them
0.6 has 1 decimal place and 0.04 has 2 decimal places — a total of 3. So the product of the digits (24) must have 3 decimal places: 0.024. The answer 0.24 only has 2 decimal places, which means the student miscounted. A quick estimate confirms: 0.6 × 0.04 ≈ 0.6 × 0 = near-zero, and 0.024 is much closer to zero than 0.24.
Question 2 Multiple Choice
Why does the total number of decimal places in the factors equal the number of decimal places in the product?
AIt is a rule that must be memorized — there is no underlying reason
BBecause each decimal factor is a whole number divided by a power of 10, so the product must be divided by the product of those same powers of 10
CBecause decimal points always shift right during multiplication
DBecause the denominators of fractions are always added together when multiplying
2.4 = 24 ÷ 10 and 1.3 = 13 ÷ 10, so 2.4 × 1.3 = (24 × 13) ÷ (10 × 10) = 312 ÷ 100 = 3.12. Dividing by 100 means moving the decimal point two places left — which is exactly the same as counting two total decimal places. The rule isn't arbitrary; it's a shorthand for this powers-of-ten reasoning. Understanding the 'why' lets you handle unusual cases like 0.003 × 0.002 confidently.
Question 3 True / False
When multiplying decimals, you should align the decimal points, just as you do when adding or subtracting decimals.
TTrue
FFalse
Answer: False
Aligning decimal points is the rule for addition and subtraction, not multiplication. When multiplying, you ignore the decimal points entirely, multiply the digits as whole numbers, then count the total decimal places in the factors and place the decimal point that many positions from the right in the product. Applying the addition rule to multiplication is one of the most common errors students make.
Question 4 True / False
For 2.4 × 1.3, the correct product has two decimal places because each factor has one decimal place.
TTrue
FFalse
Answer: True
One decimal place (in 2.4) plus one decimal place (in 1.3) equals two decimal places in the product. So 24 × 13 = 312 becomes 3.12. You can verify with estimation: 2.4 × 1.3 ≈ 2 × 1 = 2, and 3.12 is close to 2, confirming the decimal placement. If you'd placed it as 31.2 or 0.312, estimation would immediately flag the error.
Question 5 Short Answer
Explain why 0.6 × 0.04 = 0.024 using the logic of powers of ten, rather than just applying the decimal-place counting rule.
Think about your answer, then reveal below.
Model answer: 0.6 is the same as 6 ÷ 10, and 0.04 is the same as 4 ÷ 100. So 0.6 × 0.04 = (6 ÷ 10) × (4 ÷ 100) = (6 × 4) ÷ (10 × 100) = 24 ÷ 1000 = 0.024. Dividing by 1000 moves the decimal point three places to the left, which is equivalent to counting three total decimal places in the original factors (1 from 0.6, plus 2 from 0.04). The counting rule is just a shortcut for this reasoning.
Students who only memorize 'count the decimal places' are helpless when they miscount. Students who understand the powers-of-ten reasoning can reconstruct the rule from scratch — and can estimate to verify: 0.6 × 0.04 is roughly 0.6 × 0 = near zero, so an answer in the thousandths range (0.024) makes sense, while 0.24 or 24 clearly do not.