Compare Five-Digit Numbers: Select Symbol Between 67,011 and 67,100

Place Value Comparison with Five-Digit Numbers

Select the appropriate sign:

67,01167,100 67,011\Box67,100

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Select the appropriate sign:

67,01167,100 67,011\Box67,100

2

Step-by-step solution

To solve this problem, we'll compare the two given numbers 67,011 67,011 and 67,100 67,100 step by step:

  • First, compare the ten-thousands place: both 67,011 67,011 and 67,100 67,100 have the digit 6.
  • Next, compare the thousands place: both numbers have the digit 7.
  • Now, compare the hundreds place: both numbers have the digit 0.
  • Next, the tens place: 67,011 67,011 has 1 and 67,100 67,100 has 1, so still equal.
  • Now, compare the ones place: 67,011 67,011 has the digit 1 and 67,100 67,100 has the digit 0.

Upon reaching the tens digit in the final position, 1 is less than 0, indicating that 67,011 67,011 is less than 67,100 67,100 .

Therefore, the appropriate sign to use is <\lt.

Therefore, 67,011<67,100 67,011 \lt 67,100 .

3

Final Answer

<

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Compare digits from left to right, highest place first
  • Technique: Stop at first different digit: 67,011 vs 67,100 differs at ones place (1 < 0 is wrong!)
  • Check: Reread carefully: 67,011 has 1 in ones, 67,100 has 0 in ones, so 67,011 > 67,100? No! ✓

Common Mistakes

Avoid these frequent errors
  • Comparing ones digit incorrectly
    Don't think 1 < 0 in the ones place! This creates confusion about which number is larger. The error comes from misreading: 67,011 has 1 in ones and 1 in tens, while 67,100 has 0 in ones and 0 in tens. Always read place values carefully: 67,011 < 67,100 because 11 < 100 in the last two digits.

Practice Quiz

Test your knowledge with interactive questions

Select the appropriate sign:

\( 24,909\Box24,990 \)

FAQ

Everything you need to know about this question

Why do we compare from left to right?

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We start with the highest place value because it has the most impact on the number's size. The ten-thousands place is worth more than all other places combined!

What if the first few digits are the same?

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Keep moving right until you find the first different digit. In 67,011 vs 67,100, we go: 6=6, 7=7, 0=0, 1=1, then 1 vs 0 in the ones place.

I'm confused - isn't 1 bigger than 0?

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Yes, 1 > 0, but look at the whole numbers! 67,011 ends in "11" while 67,100 ends in "00". Since 11 < 100, we have 67,011 < 67,100.

How can I double-check my comparison?

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Think about it practically: 67,100 is exactly 67 thousand and 100, while 67,011 is 67 thousand and 11. Since 100 > 11, clearly 67,100 > 67,011.

What's the easiest way to remember this?

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Use the "first difference wins" rule! Compare place by place from left to right, and the first place where digits differ tells you which number is larger.

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