Specific Comparison Task with Numbers: Determine the Appropriate Sign in 400,040 □ 400,400

Number Comparison with Place Value Analysis

Select the appropriate sign:

400,040□400,400 400,040\Box400,400

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Step-by-step written solution

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1

Understand the problem

Select the appropriate sign:

400,040□400,400 400,040\Box400,400

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Step-by-step solution

To determine the appropriate sign for the expression 400,040□400,400 400,040\Box400,400 , we should compare the two numbers digit by digit from left to right:

  • Hundred-thousands place: Both numbers have a 4. So, they are equal in this place value.
  • Ten-thousands place: Both numbers have a 0. So, they are equal in this place value as well.
  • Thousands place: Both numbers have a 0. They remain equal here.
  • Hundreds place: The first number, 400,040400,040, has a 0, and the second number, 400,400400,400, has a 4. Hence, this is where the numbers differ.

In the hundreds place, the second number, 400,400, has a greater digit than the first number. Therefore,
400,040<400,400 400,040 < 400,400 .

Accordingly, the correct sign to place in the expression is <<, indicating that 400,040 is less than 400,400.

The solution to the problem is <<.

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Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare digits from left to right in each place value
  • Technique: In hundreds place, 0 < 4, so 400,040 < 400,400
  • Check: Subtract to verify: 400,400 - 400,040 = 360 (positive confirms <) ✓

Common Mistakes

Avoid these frequent errors
  • Comparing numbers by counting digits or looking at the last digits first
    Don't compare 400,040 and 400,400 by looking at the final digits (0 vs 0) = wrong conclusion! This ignores place value importance. Always compare from left to right, stopping at the first place where digits differ.

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 I start comparing from the left instead of the right?

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The leftmost digits have the highest place values! A difference in the hundreds place (like 0 vs 4) is much more important than differences in the ones place. Always work left to right.

What if the numbers have the same digits in several places?

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Keep going! Compare each place value until you find the first difference. In this problem, hundreds place (0 vs 4) is where 400,040400,040 and 400,400400,400 first differ.

Can I just subtract to compare numbers?

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Yes, that's a great check! If the result is positive, the first number is larger. If negative, the first number is smaller. Here: 400,040−400,400=−360400,040 - 400,400 = -360, so 400,040 is smaller.

How do I remember which symbol means what?

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Think of the symbol as an arrow pointing to the smaller number! In 400,040<400,400400,040 < 400,400, the arrow points left to the smaller value. The wide side always faces the larger number.

What if I get confused with big numbers like these?

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Break them down by place value! Write 400,040 as 400 thousands + 0 hundreds + 40 ones. This makes it easier to see where the numbers differ.

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