Find the Compatible Number: 7,010 < _ _ 93 < 7,100

Number Comparison with Place Value Constraints

Select a compatible number for the given range:

7,010<_ _ 93<7,100 7,010 < \_~\_~93 <7,100

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Select a compatible number for the given range:

7,010<_ _ 93<7,100 7,010 < \_~\_~93 <7,100

2

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Interpret the range 7,010<_ _ 93<7,1007,010 < \_~\_~93 < 7,100. We need to insert digits in the blanks so that the overall number is greater than 7,010 and less than 7,100.
  • Step 2: Analyze the hundreds and tens digits. The digits need to make the whole number: 7,0_937,0 \_ 93, where the _\_ denotes the undecided digits.
  • Step 3: Evaluate each option by filling it into the blanks and check if it falls within the specified range:
  • Option 1: If we try 7,3937,393, it falls outside the upper bound of 7,100.
  • Option 2: If we try 7,0_937,0 \_ 93 by assuming it as 7,0937,093, we then have 7,010<7,093<7,1007,010 < 7,093 < 7,100. Thus, it satisfies the inequality.
  • Option 3: If we try 7,2937,293, it is also beyond the upper limit of 7,100.
  • Option 4: If we adopt 7,1937,193, it also violates the upper edge of the given range.

Therefore, the most suitable number to fill in the blanks to satisfy 7,010<_ _ 93<7,1007,010 < \_~\_~93 < 7,100 is 7,07,0 . Thus, the correct choice is:

7,0 7,0

3

Final Answer

7,0 7,0

Key Points to Remember

Essential concepts to master this topic
  • Range Rule: Find digits that make the complete number fall within bounds
  • Technique: Test each option: 7,093 gives 7,010 < 7,093 < 7,100 ✓
  • Check: Verify complete 4-digit number satisfies both inequalities simultaneously ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the complete number structure
    Don't just focus on the given digits 7,0 without considering the full number 7,093! Students often forget that the blanks create a complete 4-digit number that must satisfy both inequality conditions. Always check that your complete number 7,0__93 falls between 7,010 and 7,100.

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 I use 7,3 when it gives me 7,393?

+

Because 7,393 is greater than 7,100! The problem requires the complete number to be less than 7,100. When you fill in 7,3, you get 7,393, which breaks the upper boundary.

How do I know what digits to try?

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Look at the given range boundaries: 7,010 and 7,100. Since your number starts with 7,0__93, you need the hundreds digit to keep the total under 7,100. Only 0 in the hundreds place works!

What does the underscore pattern __ 93 mean?

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The underscores represent missing digits in specific place values. The pattern shows you need to fill in the hundreds and tens places, while 93 represents the ones and tenths places.

Do I need to check both inequality signs?

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Yes, absolutely! Your number must be greater than 7,010 AND less than 7,100. Both conditions must be true simultaneously for your answer to be correct.

Can there be more than one correct answer?

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In this specific problem, only 7,0 works because it creates 7,093. Any other option (7,1, 7,2, or 7,3) creates numbers above 7,100, violating the upper boundary.

Why is 7,093 better than 7,193?

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Because 7,093 fits the range while 7,193 doesn't! Check: 7,010<7,093<7,100 7,010 < 7,093 < 7,100 is true, but 7,193<7,100 7,193 < 7,100 is false.

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