Questions: Reading and Writing Three-Digit Numbers

Question 1

A student writes the expanded form of 583 as 5 + 8 + 3. What is wrong with this?

• A. They used addition instead of multiplication
• B. They failed to honor place value — the 5 represents 500, the 8 represents 80, and the 3 represents 3, so the correct expanded form is 500 + 80 + 3
• C. They forgot to include a zero placeholder
• D. They should have written the digits in reverse order

Answer: (B)

Expanded form exists to show the true value of each digit based on its position. The digit 5 in the hundreds place is worth 500, not 5. The digit 8 in the tens place is worth 80, not 8. Writing 5 + 8 + 3 = 16, while 583 is clearly not 16. This error shows the student knows the digit symbols but hasn't applied place value thinking — expanded form's entire purpose is to make that value explicit.

Question 2

Which is the correct expanded form of 405?

• A. 4 + 0 + 5
• B. 400 + 05
• C. 400 + 5
• D. 40 + 5

Answer: (C)

In 405, the 4 is in the hundreds place (worth 400), the 0 is in the tens place (worth 0 tens = 0), and the 5 is in the ones place (worth 5). Expanded form is 400 + 0 + 5, which simplifies to 400 + 5 since adding 0 changes nothing. Option A (4+0+5) repeats the digit-not-value mistake. Option B (400+05) incorrectly writes 05, which isn't standard. Option D (40+5=45) omits the hundreds place entirely.

Question 3

'Five hundred eighty-three' and 583 represent exactly the same quantity, expressed in different forms.

• T. True
• F. False

Answer: True

True. Standard form (583), word form ('five hundred eighty-three'), and expanded form (500 + 80 + 3) are three different representations of the same number. They look different but denote the same point on the number line and the same quantity of objects. Fluency means being able to move between these forms and recognize they are equivalent.

Question 4

The correct word form for 583 is 'five hundred and eighty-three' — the word 'and' connects the hundreds to the rest.

• T. True
• F. False

Answer: False

False. In formal number naming, the word 'and' is reserved for the decimal point — it signals that a fractional part follows (as in 'five point three' becoming 'five and three tenths'). The correct word form for 583 is simply 'five hundred eighty-three.' Using 'and' in a whole number is a very common habit, but learning the convention now prepares students for decimals later.

Question 5

Why does zero in the middle of a three-digit number (like 405) matter so much? What happens if you leave it out?

Model answer: Zero is a placeholder that holds the tens position open. Without it, 405 would be written as 45, which is a completely different number (only 45, not 405). The zero communicates 'there are zero tens here' and ensures every digit sits in its correct place, preserving the hundreds value of the 4.

Place value works because each position has a fixed meaning. If you write 45 when you mean 405, you've collapsed two different positions into one, cutting the number's value by almost 90%. The placeholder zero is not 'nothing' — it's an active symbol that maintains the structural integrity of the number by keeping every digit in its rightful column.