How to Compare Multi-Digit Whole Numbers

Procedure for Comparing Numbers

1. Align Number Places: Start with the ones place digits on the right.
2. Compare Leftmost Digits: Examine the digits farthest to the left, as they represent the largest number places.
   • If they differ, the larger digit indicates the greater number.
   • If identical, move right until differing digits are found to make a comparison.

Example Comparisons

Example 1: Different Leftmost Digits

• Numbers: 329 and 495
  • Hundreds Place Comparison: 3 (300) vs. 4 (400)
  • Result: 495 is greater than 329.

Example 2: Identical Leftmost Digits

• Numbers: 856 and 842
  • Hundreds Place: Both have 8 (800).
  • Tens Place Comparison: 5 (50) vs. 4 (40)
  • Result: 856 is greater than 842.

Example 3: Identical First Two Digits

• Numbers: 249 and 246
  • Hundreds Place: Both have 2
  • Tens Place: Both have 4
  • Ones Place Comparison: 9 vs. 6
  • Result: 249 is greater than 246.

Different Number of Digits

Example 4: Unequal Lengths

• Numbers: 75 and 128
  • Comparison:
    • 128 has hundreds place; 75 does not.
  • Result: 128 is greater than 75.

Imaginary Zero Comparison

• Conceptualize 75 as having a zero in the hundreds place.
  • 128 is greater than "075" due to 100 being greater than 0.

Larger Numbers Comparison

Example 5: Comparing Large Numbers

• Numbers: 134,297 and 137,499
  • Hundred-Thousands Place: Both have 1 (100,000).
  • Ten-Thousands Place: Both have 3 (30,000).
  • Thousands Place Comparison: 4 (4,000) vs. 7 (7,000)
  • Result: 137,499 is greater than 134,297.

Conclusion

Through practice, the process of comparing multi-digit whole numbers becomes intuitive. Remember:

• Compare the leftmost digits first.
• If identical, move right to the next significant place until you find differing digits.
• Numbers with more digits inherently have greater value.

For more information and practice resources, visit mathantics.com.