Compare Numbers 17□ and 159: Finding the Missing Digit and Inequality Sign

Q: What if the missing digit was in a different position?

The position matters! If it were $ 1\Box7 $, you'd get numbers from 107 to 197, giving different comparison results. Always identify which digit position is unknown.

Q: How do I know which comparison sign to use?

Create the range of possible values first. If all values are greater than the comparison number, use >. If all are less, use

Q: What's the fastest way to solve this type of problem?

Find the smallest possible value (170 in this case)Find the largest possible value (179 in this case)If both have the same relationship to 159, that's your answer!

Number Comparison with Missing Digits

There is an unknown digit behind the $\Box$

Determine the correct sign for the following expression:

$17\Box?159$

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

There is an unknown digit behind the $\Box$

Determine the correct sign for the following expression:

$17\Box?159$

Step-by-step solution

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

Step 1: Identify the range of possible values for 17 followed by a digit (Box).
Step 2: Compare each possible value against 159.

Now, let's work through each step:

Step 1: The number 17 followed by an unknown digit can be represented as $17\Box$ , where $\Box$ can be any digit from 0 to 9. This forms the numbers 170 to 179.

Step 2: We'll compare these numbers:

$170 > 159$
$171 > 159$
$172 > 159$
$173 > 159$
$174 > 159$
$175 > 159$
$176 > 159$
$177 > 159$
$178 > 159$
$179 > 159$

Since all possible values of $17\Box$ (from 170 to 179) are greater than 159, the correct comparison sign is $>$ .

Therefore, the solution to the problem is $>$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Range Analysis: Unknown digit creates numbers from 170 to 179
Technique: Compare smallest possibility: 170 > 159, so all are greater
Check: Test both extremes: 170 > 159 and 179 > 159 ✓

Common Mistakes

Avoid these frequent errors

Testing only one possible digit value
Don't just check if 175 > 159 and assume that's the answer! The unknown digit could be any value from 0-9, giving different numbers. Always consider the complete range from 170 to 179 to ensure all possibilities lead to the same comparison result.

Practice Quiz

Test your knowledge with interactive questions

Which group contains numbers that are smaller in value than 87?

FAQ

Everything you need to know about this question

Do I need to check every single number from 170 to 179?

Not necessarily! Since all numbers starting with 17 are at least 170, and 170 > 159, you can conclude that all possibilities are greater than 159.

What if the missing digit was in a different position?

The position matters! If it were $1\Box7$ , you'd get numbers from 107 to 197, giving different comparison results. Always identify which digit position is unknown.

Could the answer ever be 'equals' for this type of problem?

Only if one of the possible numbers exactly matches the comparison number. For example, if comparing $15\Box$ to 159, then 159 would make them equal!

How do I know which comparison sign to use?

Create the range of possible values first. If all values are greater than the comparison number, use >. If all are less, use <. If the range includes both greater and less values, there's no single correct answer.

What's the fastest way to solve this type of problem?

Find the smallest possible value (170 in this case)
Find the largest possible value (179 in this case)
If both have the same relationship to 159, that's your answer!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Magnitude up to 100 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