Find Missing Digits: Complete ??98 Between 7,001 and 8,100

Number Comparison with Four-Digit Intervals

Insert the missing digits in order to obtain a number that correctly lies within the given range:

7,001<??98<8,100 7,001 < ??98 < 8,100

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Insert the missing digits in order to obtain a number that correctly lies within the given range:

7,001<??98<8,100 7,001 < ??98 < 8,100

2

Step-by-step solution

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

  • Step 1: Identify possible candidates for the missing digits.
  • Step 2: Substitute digits from the choices and check their suitability by comparing with given boundaries.

Now, let's work through each step:
Step 1: We need to find a number of the form ??98 ??98 and check possible combinations for the '?'. Given the choices, we'll consider 7,001 to 8,100 as the interval.
Step 2: Evaluate: the number should start with either 7 or 8 because 7,001 is above 7,000. Checking, 7,198 7,198 and 8,098 8,098 are obvious boundaries and choices.

Substitute option '8,0' leading to 8,098 8,098 which satisfies:
7,001<8,098<8,100 7,001 < 8,098 < 8,100 .

Therefore, the correct missing digits are 8,0 8,0 .

3

Final Answer

8,0 8,0

Key Points to Remember

Essential concepts to master this topic
  • Range Analysis: Numbers must fall strictly between 7,001 and 8,100
  • Place Value Method: Start with thousands digit: 7 or 8 only
  • Verification: Check 7,001 < 8,098 < 8,100 gives true statements ✓

Common Mistakes

Avoid these frequent errors
  • Not checking boundary conditions carefully
    Don't just pick digits that look reasonable without testing the complete number = wrong answers! Students often choose 7,998 thinking it's valid, but 7,998 > 8,100 is false. Always substitute your complete four-digit number and verify both inequality conditions.

Practice Quiz

Test your knowledge with interactive questions

Insert the missing digits in order to obtain a number that correctly lies within the given range:

\( 7,001 < ??98 < 8,100 \)

FAQ

Everything you need to know about this question

Why can't the first missing digit be 6 or 9?

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If the first digit is 6, you get 6?98 6?98 , which is less than 7,001 (violates the left boundary). If it's 9, you get 9?98 9?98 , which is greater than 8,100 (violates the right boundary).

How do I know which thousands digit to choose: 7 or 8?

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Look at the upper boundary carefully! Since we need the number to be less than 8,100, and our number ends in 98, we need 8,098. If we used 7,098, it would work too, but check the answer choices!

What if there are multiple correct answers?

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In this problem, both 7,098 7,098 and 8,098 8,098 satisfy the inequality. However, you must choose from the given options. Only (8,0) appears in the choices.

Do I need to check both inequalities?

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Yes! You must verify that your number is both greater than 7,001 AND less than 8,100. Missing either check can lead to wrong answers.

What does the comma in the answer choices mean?

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The comma separates the two missing digits. For example, (8,0) means the first missing digit is 8 and the second missing digit is 0, giving you 8,098.

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