A student compares 482 and 97 and says 97 is bigger because '9 is greater than 4.' What mistake is the student making?
AThe student is using the wrong comparison symbol
BThe student compared the wrong digit — they should compare the first digits of the longer number to get the right answer
CThe student compared individual digits without considering their place values — 482 has a hundreds digit and 97 does not, making 482 far larger
DThe student forgot to add the digits together first
The 9 in 97 is in the tens place (representing 90), while the 4 in 482 is in the hundreds place (representing 400). When comparing numbers with different numbers of digits, the number with more digits is always larger — hundreds beat tens. The student's error is cherry-picking the largest-looking digit without considering what place value it occupies.
Question 2 Multiple Choice
To compare 563 and 578, what is the correct first step?
ACompare the ones digits: 3 vs. 8
BCompare the tens digits: 6 vs. 7
CCompare the hundreds digits: 5 vs. 5
DAdd all the digits in each number and compare the sums
Always start at the leftmost (highest) place value: the hundreds. Here, both numbers have 5 hundreds, so they are equal at this position and you move to the tens. Comparing ones first or adding all digits are incorrect strategies that can give wrong results. Adding the digits (5+6+3=14 vs. 5+7+8=20) doesn't compare place values and would give nonsense comparisons.
Question 3 True / False
When comparing two three-digit numbers, you should examine most three digits before deciding which number is greater.
TTrue
FFalse
Answer: False
You only need to compare until you find a difference. If the hundreds digits differ, the comparison is done — the one with more hundreds is greater, regardless of the tens and ones. You only move to the tens if hundreds are equal, and only to ones if tens are also equal. Stopping at the first unequal digit is both faster and the logical basis of place-value comparison.
Question 4 True / False
In the comparison 741 > 389, you only need to look at the hundreds digits to determine which number is greater.
TTrue
FFalse
Answer: True
741 has 7 hundreds; 389 has 3 hundreds. Seven hundreds (700) is greater than three hundreds (300), regardless of what the tens and ones say. Once the highest place value differs, the comparison is settled. This is exactly what makes place-value notation powerful: the most significant digit tells you the most.
Question 5 Short Answer
Explain why, when comparing 741 and 389, you don't need to look at the tens or ones digits at all.
Think about your answer, then reveal below.
Model answer: The hundreds digit represents the largest value in a three-digit number. 741 has 7 hundreds (700) and 389 has only 3 hundreds (300). Even if 389 had the largest possible tens and ones (99), it would only reach 399 — still less than 700. Once you see that one number has more hundreds, no combination of tens and ones in the other number can make up the difference.
Place value is hierarchical: each position is worth ten times the position to its right. The hundreds place dominates because 1 hundred = 10 tens = 100 ones. Seeing this hierarchy is the key insight behind left-to-right comparison: the leftmost digit tells you the most, so you start there and stop as soon as you find a difference.