Find the Missing Number: 689,354 < ◻ < 710,1105

Q: How do I compare large numbers like these?

Start from the leftmost digits and compare place by place. For example, 701,106 vs 710,105: both start with 7, but the ten-thousands place shows 0

Q: What does the comma mean in these numbers?

The comma is a thousands separator. So 689,354 means 689 thousand and 354, which equals 689,354. It helps make large numbers easier to read!

Q: Why can't 720,104 be the answer even though it's bigger than 689,354?

Because 720,104 is too big! It must be less than the upper bound 710,105. Since 720,104 > 710,105, it's outside our range.

Q: How do I know which number fits in the range?

Test each option with both inequalities:Is it greater than 689,354? ✓Is it less than 710,105? ✓Only 701,106 satisfies both conditions!

Q: What if two numbers both fit in the range?

In multiple choice questions, only one answer will correctly fit the given range. If you find multiple options that work, double-check your comparisons - you might have made an error.

Number Comparison with Large Integers

Select the appropriate number for the given range:

$689,354 < \Box < 710,1105$

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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:

$689,354 < \Box < 710,1105$

Step-by-step solution

Let's solve this problem step-by-step:

To select the appropriate number within the range $689,354 < \Box < 710,105$ , we will verify each provided choice to see if it fits within these boundaries:

First choice: $720,104$
- Compare: $689,354 < 720,104$ (True) and $720,104 < 710,105$ (False)
- Conclusion: $720,104$ is not in the range.
Second choice: $689,104$
- Compare: $689,354 < 689,104$ (False)
- Conclusion: $689,104$ is not in the range.
Third choice: $701,106$
- Compare: $689,354 < 701,106$ (True) and $701,106 < 710,105$ (True)
- Conclusion: $701,106$ is in the range.
Fourth choice: $711,107$
- Compare: $711,107 < 710,105$ (False)
- Conclusion: $711,107$ is not in the range.

Thus, the only choice that satisfies the condition $689,354 < \Box < 710,105$ is $701,106$ .

Therefore, the solution to the problem is $701,106$ .

Final Answer

$701,106$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare numbers digit by digit from left to right
Technique: Check both inequalities: 689,354 < 701,106 and 701,106 < 710,105
Check: Verify both boundaries are satisfied for the chosen number ✓

Common Mistakes

Avoid these frequent errors

Only checking one inequality instead of both
Don't just verify 689,354 < 701,106 and ignore the upper bound = wrong answer selection! This misses numbers outside the complete range. Always check both inequalities: the number must be 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 these?

Start from the leftmost digits and compare place by place. For example, 701,106 vs 710,105: both start with 7, but the ten-thousands place shows 0 < 1, so 701,106 < 710,105.

What does the comma mean in these numbers?

The comma is a thousands separator. So 689,354 means 689 thousand and 354, which equals 689,354. It helps make large numbers easier to read!

Why can't 720,104 be the answer even though it's bigger than 689,354?

Because 720,104 is too big! It must be less than the upper bound 710,105. Since 720,104 > 710,105, it's outside our range.

How do I know which number fits in the range?

Test each option with both inequalities:

Is it greater than 689,354? ✓
Is it less than 710,105? ✓

Only 701,106 satisfies both conditions!

What if two numbers both fit in the range?

In multiple choice questions, only one answer will correctly fit the given range. If you find multiple options that work, double-check your comparisons - you might have made an error.

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