Questions: Place Value and Expanded Form

Question 1

What is the value of the digit 5 in the number 532?

• A. 5, because 5 is the digit itself
• B. 50, because 5 is in the tens place
• C. 500, because 5 is in the hundreds place
• D. 5,000, because it is the leading digit

Answer: (C)

In 532, the 5 is in the hundreds place, so its value is 5 × 100 = 500. The digit 5 looks the same everywhere, but its position determines what it is worth. Position is everything in a place value system. If the 5 were in the tens place (as in 253), it would be worth 50; in the ones place (as in 235), it would be worth just 5. Expanded form makes this visible: 532 = 500 + 30 + 2.

Question 2

What is the correct expanded form of 305, and what does the zero in the tens place tell you?

• A. 300 + 50 + 0 — the zero holds the ones place and 5 is in the tens place
• B. 300 + 0 + 5 — the zero means there are no tens; the 5 is in the ones place
• C. 30 + 5 — zeros can be dropped from expanded form because they add nothing
• D. 300 + 5 — the zero is just a placeholder and doesn't affect other digits' values

Answer: (B)

305 = 300 + 0 + 5. The zero in the tens place is critical: it shows that there are no tens in this number. Without the zero, 305 and 35 would look the same in some notations — the zero holds the tens place so that the 3 stays in the hundreds position and the 5 stays in the ones position. Expanded form for 305 is written as 300 + 0 + 5, making explicit that the tens value is 0 × 10 = 0.

Question 3

The digit 7 represents a different value in 70 than it does in 700.

• T. True
• F. False

Answer: True

True. In 70, the 7 is in the tens place, so it is worth 7 × 10 = 70. In 700, the 7 is in the hundreds place, so it is worth 7 × 100 = 700. The same digit, placed in different positions, represents quantities ten times apart. This is the fundamental principle of the place value system: position determines value. Expanded form makes both values visible: 70 = 70 + 0, and 700 = 700 + 0 + 0.

Question 4

In the number 234, the digit 2 has a value of 2.

• T. True
• F. False

Answer: False

False. In 234, the digit 2 is in the hundreds place, so its value is 2 × 100 = 200. The digit 2 represents two hundred, not two. Students who say 'the 2 is worth 2' are reading the digit without considering its position. Expanded form — 234 = 200 + 30 + 4 — makes this explicit. The whole point of expanded form is to reveal what each digit is actually worth based on where it sits.

Question 5

Explain why expanded form is more than just a notation exercise — how does understanding expanded form connect to doing addition with multi-digit numbers?

Model answer: Expanded form reveals that multi-digit addition is really place-by-place addition. When you add 234 + 153, you are adding the hundreds (200 + 100 = 300), the tens (30 + 50 = 80), and the ones (4 + 3 = 7) separately, then combining: 300 + 80 + 7 = 387. Every column in the standard addition algorithm corresponds to one position in expanded form.

The column-by-column structure of the standard addition algorithm is directly an application of expanded form: you add the ones column, then the tens column, then the hundreds column — each column corresponds to one addend in the expanded representation. Understanding expanded form prevents students from treating multi-digit numbers as sequences of unrelated digits. It shows that 234 is not 'two, three, four' but 'two hundred plus thirty plus four' — a sum whose parts can be operated on independently and then recombined.