Questions: Tens and Ones Place Value

Question 1

In the number 35, what is the value of the digit 3?

• A. 3 — it just means three
• B. 30 — it represents three tens
• C. 300 — it represents three hundreds
• D. The value depends on which digit comes next

Answer: (B)

The 3 in 35 is in the tens place, so it means three tens, which equals 30. The digit 3 by itself means 'three,' but its position in a number is what determines its actual value. This is the heart of place value: the same digit means different amounts depending on where it sits in the number.

Question 2

A student says: '17 is made of the numbers 1 and 7, so it equals 1 + 7 = 8.' What is wrong with this reasoning?

• A. Nothing — 17 is indeed 1 plus 7
• B. The 1 represents one ten (10), not just one, so 17 = 10 + 7 = 17
• C. You should multiply: 1 × 7 = 7
• D. The order of digits doesn't matter in addition

Answer: (B)

The student is treating each digit as its face value and ignoring position. The 1 in 17 is in the tens place, so it represents one ten (the value 10), not just the number 1. The correct decomposition is 17 = 10 + 7. This is the classic misconception: seeing digits as isolated numbers rather than as place-value representations.

Question 3

In the number 71, the digit 7 has a smaller value than the digit 7 in the number 17.

• T. True
• F. False

Answer: False

The 7 in 71 is in the tens place, giving it a value of 70. The 7 in 17 is in the ones place, giving it a value of 7. So the 7 in 71 is actually ten times larger. This illustrates why position matters so much — the same digit 7 can represent 7 or 70 or 700 depending on its place in the number.

Question 4

Ten individual unit blocks can be traded for one ten-rod without changing the total amount.

• T. True
• F. False

Answer: True

Ten ones and one ten represent exactly the same quantity — they are just packaged differently. A ten-rod is literally made of ten units fused together. This equivalence (10 ones = 1 ten) is the core mechanical insight that makes regrouping in addition and subtraction possible. Understanding that you can trade between forms without changing the total is what makes borrowing and carrying make sense.

Question 5

Why does the position of a digit in a number matter? Why isn't the digit 3 always just worth 3?

Model answer: In our base-ten system, each position has a different value. The ones place is worth 1, the tens place is worth 10, and the hundreds place is worth 100. A digit in any position is multiplied by that position's value. So 3 in the ones place = 3, but 3 in the tens place = 30, and 3 in the hundreds place = 300. Without position mattering, numbers like 35 and 53 would be the same, which they clearly are not.

This is the fundamental principle of positional notation, the system that underlies all of our arithmetic. Understanding it converts numbers from memorized symbols into meaningful structures that can be decomposed, compared, and operated on with understanding.