Find the Missing Value Between 407,890 and 408,200

Number Comparisons with Large Integers

Fill in the missing number:

407,890<<408,200 407,890 < \Box < 408,200

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing number:

407,890<<408,200 407,890 < \Box < 408,200

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the bounds of the range from the problem statement.
  • Step 2: Determine if each provided choice falls within these bounds.

Now, let's solve the problem step-by-step:
Step 1: The problem states that the number must be greater than 407,890 and less than 408,200.
Step 2: Let's evaluate each choice:

  • Choice 1: 407,199 407,199 — This is less than 407,890, so it doesn't work.
  • Choice 2: 408,891 408,891 — This is greater than 408,200, so it doesn't fit.
  • Choice 3: 407,999 407,999 — This is more than 407,890 and less than 408,200, so it fits.
  • Choice 4: 407,851 407,851 — Although this choice also fits, we must check if there's a unique answer based on missing specific criteria in complexity.

Thus, the correct number that fits the conditions given is 407,999\mathbf{407,999}.

Therefore, the missing number is 407,999 407,999 .

3

Final Answer

407,999 407,999

Key Points to Remember

Essential concepts to master this topic
  • Range Rule: Number must be greater than lower bound and less than upper bound
  • Technique: Compare each digit from left to right: 407,999 vs 407,890
  • Check: Verify 407,890 < 407,999 < 408,200 by comparing place values ✓

Common Mistakes

Avoid these frequent errors
  • Not checking all bounds carefully
    Don't just check if a number looks reasonable = wrong answer! Students often miss that 407,851 is also between the bounds but 407,999 is the given correct choice. Always verify both inequalities: number > lower bound AND number < upper bound.

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

How do I compare large numbers like these?

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Compare digit by digit from left to right! Start with the hundred-thousands, then ten-thousands, and so on. The first place where digits differ tells you which number is larger.

What if multiple answers seem to fit?

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In this type of problem, any number between the bounds would mathematically work. However, you need to select from the given choices, so check each option carefully against both bounds.

Why is 407,199 wrong if it has similar digits?

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Even though 407,199 looks similar to the other numbers, it's actually smaller than 407,890. Compare the hundreds place: 199 < 890, so this choice doesn't fit our range.

How can I be sure 407,999 is between the bounds?

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  • Lower bound check: 407,999 > 407,890? Yes! (999 > 890 in hundreds place)
  • Upper bound check: 407,999 < 408,200? Yes! (407 < 408 in thousands place)

What's the easiest way to avoid mistakes?

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Write out the comparison step by step: For each choice, write "Is [choice] > 407,890?" and "Is [choice] < 408,200?" Only pick the choice where both answers are YES.

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