Identify the Number that Completes the Inequality: 560,979 < ? < 561,949

Q: How do I compare large numbers quickly?

Start from the leftmost digits and work right. If the thousands place is different, that determines which number is larger. For example, 561,000 is automatically larger than 560,999 because of the thousands digit.

Q: What if two numbers look very similar?

Focus on the first digit that's different. In 561,003 vs 561,949, both start with 561, but the hundreds place differs: 0

Q: Why can't 561,980 be the answer?

Because $ 561,980 > 561,949 $! The number must be less than 561,949, not greater than it. Always check both boundaries carefully.

Q: What's the easiest way to avoid mistakes?

Write it out: 560,979 Test each option: Is it bigger than the left? Smaller than the right?Double-check: Read the inequality symbols carefully!

Number Comparison with Large Integers

Fill in the missing number:

$560,979 < \Box < 561,949$

❤️ 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

Fill in the missing number:

$560,979 < \Box < 561,949$

Step-by-step solution

To solve this problem, let's verify which number fits within the range.

We are given the inequality: $560,979 < \Box < 561,949$ .
We must find a number that satisfies this inequality.

Now, examining each choice:

Choice 1: $561,980$ - This number is greater than $561,949$ , so it does not satisfy the condition.
Choice 2: $561,999$ - This number is also greater than $561,949$ , so it again does not satisfy the condition.
Choice 3: $561,003$ - This number is greater than $560,979$ and less than $561,949$ , thus it satisfies the condition.
Choice 4: $560,003$ - This number is less than $560,979$ , and thus it does not satisfy the condition.

Based on the analysis of each choice, the number that falls within the specified range is:

Therefore, the solution to the problem is $561,003$ .

Final Answer

$561,003$

Key Points to Remember

Essential concepts to master this topic

Inequality Rule: The number must be greater than the left value
Technique: Compare each digit position: 561,003 > 560,979 and < 561,949
Check: Verify both conditions: 560,979 < 561,003 < 561,949 ✓

Common Mistakes

Avoid these frequent errors

Only checking one side of the inequality
Don't just verify that 561,003 > 560,979 and ignore the upper bound = wrong answer! This leads to selecting numbers outside the valid range. Always check that your number satisfies BOTH parts of the 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

How do I compare large numbers quickly?

Start from the leftmost digits and work right. If the thousands place is different, that determines which number is larger. For example, 561,000 is automatically larger than 560,999 because of the thousands digit.

What if two numbers look very similar?

Focus on the first digit that's different. In 561,003 vs 561,949, both start with 561, but the hundreds place differs: 0 < 9, so 561,003 is smaller.

Why can't 561,980 be the answer?

Because $561,980 > 561,949$ ! The number must be less than 561,949, not greater than it. Always check both boundaries carefully.

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

No! Any number between 560,979 and 561,949 would work. For example: 561,000, 561,500, or 561,800. The question asks you to identify which given option fits the range.

What's the easiest way to avoid mistakes?

Write it out: 560,979 < ? < 561,949
Test each option: Is it bigger than the left? Smaller than the right?
Double-check: Read the inequality symbols carefully!

🌟 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