Questions: Comparing and Ordering Three-Digit Quantities

Question 1

A student compares 482 and 479 and concludes '479 is greater because 79 is greater than 82.' What error did the student make?

• A. No error — comparing the last two digits is a valid method for three-digit numbers
• B. The student compared the tens and ones digits while ignoring the hundreds; since both numbers have the same hundreds digit (4), you compare the tens: 8 > 7, so 482 > 479
• C. The student should have compared the ones digits first, then moved left
• D. The student should have added all the digits in each number before comparing

Answer: (B)

The correct method is left-to-right comparison: hundreds first, then tens (only if hundreds tie), then ones (only if tens also tie). Both numbers have 4 hundreds, so move to the tens: 8 tens vs. 7 tens — 8 wins, so 482 > 479. Comparing the two-digit endings (82 vs. 79) looks plausible because it gives the right answer here — but it breaks down with other numbers and misunderstands why place value works the way it does.

Question 2

You need to order 523, 532, and 519 from least to greatest. What is the correct first step?

• A. Compare the ones digits of all three numbers first, since they differ the most
• B. Add all the digits of each number and compare the sums
• C. Compare the hundreds digits; if equal, compare tens digits; if still equal, compare ones digits
• D. Look for the largest individual digit anywhere in any of the numbers

Answer: (C)

Always start at the leftmost (most powerful) digit — the hundreds place. All three numbers have 5 hundreds, so move to the tens: 2 vs. 3 vs. 1. Ordering by tens gives 519 (1 ten) < 523 (2 tens) < 532 (3 tens). The ones digits never need to be compared here because the tens already differentiate all three. Starting at the ones digit (option A) would give a wrong ordering in many cases.

Question 3

When comparing 347 and 291, it is necessary to look at the tens and ones digits to determine which number is greater.

• T. True
• F. False

Answer: False

The hundreds digit is decisive: 3 hundreds vs. 2 hundreds — 3 wins, so 347 > 291 immediately. You never need to look at the tens or ones digits because no combination of tens and ones in a three-digit number can compensate for a deficit of one full hundred. (The maximum value of the tens and ones places combined is 99, which is less than 100.) You stop as soon as you find a differing digit, moving left to right.

Question 4

The symbol < always points toward the smaller number in a comparison.

• T. True
• F. False

Answer: True

The < and > symbols both 'open' toward the larger value, meaning the pointed tip aims at the smaller one. In 318 < 472, the tip of < points at 318 (the smaller number) and opens toward 472 (the larger). One memory trick: the symbol is like a hungry mouth that eats the bigger number — it always opens toward the greater value, with the tip pointing at the lesser.

Question 5

Explain why you always start comparing at the hundreds place (leftmost digit) when comparing three-digit numbers. What would go wrong if you started with the ones place instead?

Model answer: The hundreds place is the most powerful: a single hundred is worth more than any possible combination of tens and ones (the max is 9 tens + 9 ones = 99, which is less than 100). If one number has more hundreds than another, it is automatically greater — no other digits matter. Starting with the ones place gives the wrong result whenever the higher-place digits differ. For example, comparing 700 and 199 by ones digits gives 0 vs. 9, incorrectly suggesting 199 is greater.

Place value is a positional system where each position to the left is worth 10 times more than the position to the right. Comparison must proceed from most valuable to least valuable because the higher place will always override whatever the lower places say. This same logic extends to larger numbers: you always compare digits left to right, stopping the moment you find a position where the digits differ.