Comparing and Ordering Multi-Digit Numbers for 4th Grade
Comparing and ordering multi-digit numbers is a key skill in Grade 4. Students learn to use place value to tell which number is greater or less: compare the digits from left to right (largest place first). When two numbers have the same number of digits, we compare the first digit; if they are equal, we move to the next place until we find a difference.
Ordering means arranging numbers from least to greatest or greatest to least. This skill is used when reading data, solving word problems, and checking answers. Comparing and ordering build directly on a solid understanding of place value through hundred thousands.
DETAILED EXPLANATION
To compare two whole numbers: First, check the number of digits. A number with more digits is always greater (e.g., 5,000 is greater than 999). If both numbers have the same number of digits, compare the digits from left to right. The first place where the digits differ tells you which number is greater. For example, 47,382 and 47,592: both have 5 digits. Ten thousands: 4 and 4 (same). Thousands: 7 and 7 (same). Hundreds: 3 and 5. Since 5 > 3, we know 47,592 > 47,382.
The symbols we use: > means “greater than,” < means "less than," and = means "equal to." To order three or more numbers, compare them in pairs or find the smallest (or largest) first, then the next, and so on.
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WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS
Example 1
Compare: 62,450 and 62,405. Which is greater?
Solutions:
Step 1: Both numbers have 5 digits. Compare from left to right. Ten thousands: 6 and 6 (same). Thousands: 2 and 2 (same). Hundreds: 4 and 4 (same). Tens: 5 and 0. So 5 > 0.
Step 2: The first difference is in the tens place. 62,450 has 5 tens; 62,405 has 0 tens. So 62,450 is greater.
Answer: 62,450 > 62,405
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