Questions: Three-Digit Place Value

Question 1

In the number 347, what is the value of the digit 3?

• A. 3 — that is the digit itself
• B. 30 — it is the second-largest digit in the number
• C. 300 — it is in the hundreds place
• D. 3,000 — there are three digits following it

Answer: (C)

The digit 3 is in the hundreds place, so its value is 3 × 100 = 300. This is the core idea of a positional number system: the same digit has a different value depending on its position. The digit 3 in 347 contributes 300 to the total, not 3.

Question 2

Which correctly represents 305 in expanded form?

• A. 30 + 5
• B. 300 + 50 + 5
• C. 300 + 5
• D. 3 + 0 + 5

Answer: (C)

305 = 3 hundreds + 0 tens + 5 ones = 300 + 0 + 5 = 300 + 5. Option A (30 + 5 = 35) places the 3 in the tens position instead of hundreds. Option B (300 + 50 + 5 = 355) incorrectly assigns 50 to the tens place when there is a 0 there. Option D treats each digit as its face value instead of its positional value.

Question 3

The 0 in 507 is a placeholder that prevents the number from being misread as 57.

• T. True
• F. False

Answer: True

True. The 0 in 507 holds the tens place open, keeping the 5 in the hundreds place and the 7 in the ones place. Without it, the number would collapse to 57 — five tens and seven ones — which is entirely different. Zero as a placeholder is essential to a positional number system.

Question 4

In the number 263, the digit 2 has a smaller value than the digit 6.

• T. True
• F. False

Answer: False

False. The digit 2 is in the hundreds place, giving it a value of 200. The digit 6 is in the tens place, giving it a value of 60. 200 > 60, so the digit 2 represents a larger portion of the number than the digit 6, even though 6 > 2 as raw face values. Position determines value.

Question 5

What does it mean to say our number system is 'positional'? Use the number 444 to illustrate your answer.

Model answer: In a positional system, a digit's value depends on where it appears, not just what digit it is. In 444, every digit is 4, but the leftmost 4 is worth 400 (hundreds place), the middle 4 is worth 40 (tens place), and the rightmost 4 is worth 4 (ones place). The same digit has three different values because of its position.

444 = 400 + 40 + 4, all from the same digit in three different positions. This is why we call it a 'place value' system — the digit is just a symbol, and its position multiplies it by 1, 10, 100, and so on.