Questions: Multiplying by Multiples of Ten

Question 1

A student calculates 0.5 × 10 by 'adding a zero' and writes the answer as 0.50. What is the correct answer, and why does the shortcut fail here?

• A. 0.50 — adding a zero is always the correct method for multiplying by 10
• B. 5 — the digit 5 shifts one place to the left, from tenths to ones
• C. 0.510 — you insert the zero after the 5 in the decimal
• D. 50 — any multiplication by 10 moves the answer past the decimal point

Answer: (B)

Multiplying by 10 is a place-value shift: every digit moves one column to the left. The 5 in the tenths place (0.5) shifts to the ones place, giving 5. 'Adding a zero' only mimics this shift for whole numbers — it fails with decimals because writing 0.50 doesn't actually change the value (0.5 = 0.50). Understanding the digit-shift principle, not the zero-appending shortcut, is what survives into decimal arithmetic.

Question 2

What is 600 × 70?

• A. 4,200 — multiply 6 × 7, then add only the zeros from one factor
• B. 420 — multiply 6 × 7, keep one zero
• C. 42,000 — multiply 6 × 7 = 42, then add the three total trailing zeros
• D. 420,000 — count all digits, not just zeros

Answer: (C)

Strip the trailing zeros (two from 600, one from 70), multiply the remaining digits (6 × 7 = 42), then reattach all three zeros: 42,000. The zero-counting step is where errors cluster — be deliberate. Option A only adds zeros from one factor; option D overcounts by including non-zero digits.

Question 3

When you multiply 4 × 300, the digit 4 effectively shifts two places to the left, producing 1,200.

• T. True
• F. False

Answer: True

4 × 300 = 4 × (3 × 100). First 4 × 3 = 12, then 12 × 100 shifts every digit of 12 two places left: 1,200. The place-value shift model fully explains the result. The leading digits 1 and 2 have moved left twice relative to where 4 started.

Question 4

The 'add a zero' shortcut for multiplying by 10 works for most type of number, including decimals.

• T. True
• F. False

Answer: False

The shortcut works only for whole numbers. For decimals, 'adding a zero' to 0.5 gives 0.50, which equals 0.5 — unchanged. The actual operation is a place-value shift, and that shift must be performed correctly regardless of number type. Memorizing the shortcut without understanding why it works leaves students stranded when decimals appear.

Question 5

Explain why the 'add a zero' shortcut works for whole numbers but fails for 0.5 × 10.

Model answer: For whole numbers, appending a zero shifts all digits one place to the left and fills the now-empty ones place with a zero placeholder — which is exactly what multiplying by 10 does. But for 0.5, the digit 5 is in the tenths place. Multiplying by 10 shifts it left to the ones place, giving 5. Writing '0.50' doesn't shift anything — it just adds a meaningless trailing zero. The digit-shift is the real operation; 'add a zero' is only a coincidental side-effect that works when the ones place was previously occupied.

The misconception is treating the shortcut as the rule instead of as a consequence of place-value shifting. Students who understand the underlying mechanism can handle any variant — decimals, large numbers, chains of multiples — without needing a separate rule for each case.