Questions: Comparing and Ordering Three-Digit Numbers

Question 1

A student compares 356 and 419. She says 356 is greater because it has a 5 in the tens place and 419 only has a 1. What is wrong with this reasoning?

• A. She is correct — the tens digit is the most important digit
• B. She forgot to also check the ones place
• C. She compared tens first, but hundreds must be checked first — 419 has 4 hundreds and 356 has 3 hundreds, so 419 is greater
• D. She should add all the digits together to compare

Answer: (C)

The hundreds place is always checked first when comparing three-digit numbers. 419 has 4 hundreds (400) and 356 has 3 hundreds (300). Since 4 > 3, 419 is greater — the tens and ones digits are irrelevant. The hundreds place contributes up to 900 to a number's value, while tens and ones together contribute at most 99. A single hundreds difference always overrules any combination of lower digits.

Question 2

Put these numbers in order from least to greatest: 743, 128, 734

• A. 128, 743, 734
• B. 128, 734, 743
• C. 734, 128, 743
• D. 734, 743, 128

Answer: (B)

First, 128 has 1 hundred — clearly smallest. Then compare 743 and 734: both have 7 hundreds (tied), so move to tens. 743 has 4 tens; 734 has 3 tens. Since 4 > 3, 743 > 734. Correct order: 128, 734, 743. The three-step process — compare hundreds, then tens, then ones — is applied one place at a time, stopping as soon as a difference is found.

Question 3

When comparing 503 and 498, the hundreds digit alone tells you which number is greater without needing to look at the tens or ones.

• T. True
• F. False

Answer: True

503 has 5 hundreds; 498 has 4 hundreds. Since 5 > 4, 503 > 498, regardless of what the tens and ones say. You never need to examine lower place values when a higher place value has already decided the comparison. The ones digit 3 vs. 8 is irrelevant here.

Question 4

A number with a 9 in the ones place is typically greater than a number with a 1 in the ones place.

• T. True
• F. False

Answer: False

The ones place is the least important position. For example, 201 > 199, even though 199 has a 9 in the ones place and 201 has only a 1. The hundreds digit (2 vs. 1) determines the comparison before the ones digit is ever considered. Higher place values always override lower ones.

Question 5

If two three-digit numbers have different hundreds digits, do you need to look at the tens or ones digits to determine which is greater? Explain why.

Model answer: No. If the hundreds digits differ, the number with the larger hundreds digit is greater — period. The hundreds place contributes up to 900 to a number's value, while tens and ones together contribute at most 99. A difference of just 1 hundred (100) is always more than the maximum possible contribution from tens and ones combined.

Place value is a strict hierarchy. Each place is worth ten times the place to its right, so a larger digit in a higher position always wins. The ones and tens digits only matter as tiebreakers when the higher digits are equal.