Solve the Inequality: Find the Missing Number in 201,235 < □ < 203,100

Q: How do I compare large numbers like 201,235 and 201,999?

Start from the leftmost digits and compare place by place. Since both start with 201, look at the next digits: 235 vs 999. Since 999 > 235, we know $ 201,999 > 201,235 $.

Q: What if multiple answers seem to fit in the range?

Check each option carefully! In this problem, only one number actually fits between 201,235 and 203,100. The others are either too small or too large.

Q: Why can't 203,999 be the answer if it's close to 203,100?

Close doesn't count in inequalities! The symbol strictly less than, so 203,999 is too big because 203,999 > 203,100.

Q: Is there only one correct answer for this type of problem?

When given multiple choice options, yes - only one will fit the range. But remember, infinitely many numbers could work (like 202,000 or 201,500) if you weren't limited to the given choices.

Q: How can I double-check my answer quickly?

Use the sandwich method: write your chosen number between the two boundary numbers and verify: 201,235

Inequality Comparisons with Large Numbers

Fill in the missing number:

$201,235 < \Box < 203,100$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing number:

$201,235 < \Box < 203,100$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the range within which the missing number must lie. The given range is from $201,235$ to $203,100$ .
Step 2: Assess each multiple-choice option provided to see if it falls within this range.

Let's analyze each choice:

Choice 1: $201,999$ — Since $201,235 < 201,999 < 203,100$ , this number lies within the range.
Choice 2: $203,999$ — This number is greater than $203,100$ and does not fit within the range.
Choice 3: $200,999$ — This number is less than $201,235$ and does not fit within the range.
Choice 4: $201,099$ — This number is less than $201,235$ and does not fit within the range.

Therefore, the correct number that fits within the given constraints is $\mathbf{201,999}$ .

Hence, the solution to the problem is: $\Box = 201,999$ .

Final Answer

$201,999$

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: Check each option: 201,999 is between 201,235 and 203,100
Check: Verify 201,235 < 201,999 < 203,100 by comparing place values ✓

Common Mistakes

Avoid these frequent errors

Not checking if the number fits both inequality conditions
Don't just pick a number that looks close = it might be outside the range! Students often choose 203,999 because it's close to 203,100, but it's actually too large. Always verify the number is greater than the lower bound AND less than the 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 201,235 and 201,999?

Start from the leftmost digits and compare place by place. Since both start with 201, look at the next digits: 235 vs 999. Since 999 > 235, we know $201,999 > 201,235$ .

What if multiple answers seem to fit in the range?

Check each option carefully! In this problem, only one number actually fits between 201,235 and 203,100. The others are either too small or too large.

Why can't 203,999 be the answer if it's close to 203,100?

Close doesn't count in inequalities! The symbol < means strictly less than, so 203,999 is too big because 203,999 > 203,100.

Is there only one correct answer for this type of problem?

When given multiple choice options, yes - only one will fit the range. But remember, infinitely many numbers could work (like 202,000 or 201,500) if you weren't limited to the given choices.

How can I double-check my answer quickly?

Use the sandwich method: write your chosen number between the two boundary numbers and verify: 201,235 < 201,999 < 203,100. Both inequalities must be true!

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