Finding the Right Number: Identify the Solution Within 101,000 < ◻ < 111,010

Q: What does the symbol < mean exactly?

The symbol "less than". So \( 101,000 means the mystery number must be greater than 101,000, and \( \Box means it must be less than 111,010.

Q: Why isn't 111,099 the correct answer?

Even though 111,099 is greater than 101,000, it fails the second condition! Since 111,099 > 111,010, it doesn't satisfy \( \Box . Both conditions must be true.

Q: How do I remember which way the inequality signs point?

Think of the inequality sign as a hungry mouth that always wants to eat the bigger number! So "eats" the number on the left.

Q: Can the number equal exactly 101,000 or 111,010?

No! The inequalities use strictly less than. So the number must be between these values but cannot equal either boundary value.

Q: What if multiple answers seem to fit?

Always test each option systematically. Write out both inequalities for each choice: is it > 101,000 AND

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

Use the "sandwich test": place your answer between the two boundary numbers and see if it makes sense. \( 101,000 - yes, 101,999 fits perfectly in the middle!

Number Comparison with Range Inequalities

Select the appropriate number for the given range:

$101,000 < \Box < 111,010$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Select the appropriate number for the given range:

$101,000 < \Box < 111,010$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Review the given choices.
Step 2: Compare each choice against the range $101,000 < \Box < 111,010$ .
Step 3: Select the correct number within this range.

Let's work through these steps:

Step 1: Refer to the choices provided:
- $111,100$
- $111,099$
- $101,999$
- $120,003$

Step 2: Now, check each one to see if they fall within the range:

$111,100$ is greater than 111,010, so it does not satisfy $\Box < 111,010$ .
$111,099$ is greater than 111,010, so it does not satisfy $\Box < 111,010$ .
$101,999$ : This number is more than 101,000 and less than 111,010. Therefore, it fits the criteria.
$120,003$ is greater than 111,010, so it does not satisfy $\Box < 111,010$ .

Step 3: After reviewing all the choices, we find that the correct number that fits within the specified range is:

$101,999$

Final Answer

$101,999$

Key Points to Remember

Essential concepts to master this topic

Rule: Check both upper and lower bounds when evaluating inequalities
Technique: Compare each option: 111,100 > 111,010 (too big)
Check: Verify 101,000 < 101,999 < 111,010 are both true ✓

Common Mistakes

Avoid these frequent errors

Only checking one inequality condition
Don't just verify that a number is greater than 101,000 and ignore the upper bound = wrong answer! You might pick 111,100 which satisfies the first condition but fails the second. Always check that your number satisfies BOTH conditions in the compound inequality.

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

What does the symbol < mean exactly?

The symbol < means "less than". So $101,000 < \Box$ means the mystery number must be greater than 101,000, and $\Box < 111,010$ means it must be less than 111,010.

Why isn't 111,099 the correct answer?

Even though 111,099 is greater than 101,000, it fails the second condition! Since 111,099 > 111,010, it doesn't satisfy $\Box < 111,010$ . Both conditions must be true.

How do I remember which way the inequality signs point?

Think of the inequality sign as a hungry mouth that always wants to eat the bigger number! So < "eats" the number on the right (which is bigger), and > "eats" the number on the left.

Can the number equal exactly 101,000 or 111,010?

No! The inequalities use < (not ≤), which means strictly less than. So the number must be between these values but cannot equal either boundary value.

What if multiple answers seem to fit?

Always test each option systematically. Write out both inequalities for each choice: is it > 101,000 AND < 111,010? Only one option will satisfy both conditions.

How can I double-check my answer quickly?

Use the "sandwich test": place your answer between the two boundary numbers and see if it makes sense. $101,000 < 101,999 < 111,010$ - yes, 101,999 fits perfectly in the middle!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Magnitude up to a Million questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime