Questions: Decomposing Three-Digit Numbers by Place Value

Question 1

A student looks at the number 352 and says 'the 3 is worth 3.' Is the student correct?

• A. Yes — a digit always has the value shown, regardless of its position
• B. No — the 3 is in the hundreds place, so it represents 3 × 100 = 300
• C. Yes — place value only changes the value of 0, which becomes a placeholder
• D. No — in a three-digit number, every digit is worth ten times its face value

Answer: (B)

A digit's value depends entirely on its position (place), not just its face. The 3 in 352 sits in the hundreds place, making it worth 300. This is the core concept of place value. Option D is partially right in spirit (each place is 10× the one to its right) but too broad — the ones digit is always worth its face value.

Question 2

Which of the following correctly shows the expanded form of 405?

• A. 4 + 0 + 5
• B. 40 + 5
• C. 400 + 0 + 5
• D. 400 + 50

Answer: (C)

405 decomposes as 4 hundreds + 0 tens + 5 ones = 400 + 0 + 5. Option A shows face values, not place values (4 ≠ 400). Option B omits the hundreds place entirely. Option D incorrectly assigns 50 to the tens place when there are actually 0 tens. The zero is crucial — it holds the 4 in the hundreds place and the 5 in the ones place.

Question 3

The number 305 and the number 35 represent the same value because both contain the digits 3 and 5.

• T. True
• F. False

Answer: False

305 = 300 + 0 + 5; 35 = 30 + 5. These are completely different numbers. The zero in 305 is a placeholder that places the digit 3 in the hundreds position. Remove the zero and the 3 drops from the hundreds place to the tens place, changing the number entirely. Same digits, different positions, different values.

Question 4

247 and 200 + 40 + 7 are two different ways of writing exactly the same number.

• T. True
• F. False

Answer: True

Standard form (247) and expanded form (200 + 40 + 7) represent identical values — they are just different notations. Expanded form reveals the place-value structure; standard form is compact. Converting between them doesn't change the number, only how it is written.

Question 5

Why does the digit 0 in a three-digit number matter, even though it contributes zero value?

Model answer: Zero acts as a placeholder — it signals that there are no units of that denomination, but it also holds all other digits in their correct positions. In 305, the zero keeps the 3 in the hundreds place and the 5 in the ones place. Without the zero, you would have 35 — a completely different number. Zero's job is to preserve the positional meaning of surrounding digits, not to add value.

This is the trickiest case in three-digit decomposition. Students who understand non-zero digits sometimes still write 305 as '35' or '3 + 5 = 8' because zero 'doesn't count.' But the zero is doing critical work: it is the reason 305 is three hundred five and not thirty-five.