Find a Number Between 0.98 and 1: Decimal Inequality Problem

Q: Why can't I choose 0.98 or 1 as the answer?

The inequality uses , not ≤. This means the number must be greater than 0.98 but less than 1, excluding both endpoints.

Q: Are there other numbers that work besides 0.99?

Yes! Any decimal between 0.98 and 1 works: 0.981, 0.985, 0.99, 0.995, 0.999, etc. There are actually infinitely many correct answers!

Q: How do I compare decimals to check if they're in the right range?

Compare place by place from left to right. For 0.99: it's greater than 0.98 (9 > 8 in hundredths place) and less than 1.00 (0.99

Q: What's the difference between < and ≤?

(boundary not included), while ≤ means less than or equal (boundary included). Always check which symbol is used!

Q: Can I write 1 as 1.00 to make comparison easier?

Absolutely! Adding zeros after the decimal point doesn't change the value: 1 = 1.0 = 1.00 = 1.000. This makes decimal comparisons much clearer.

Decimal Inequalities with Boundary Exclusion

Select a compatible number for the given range:

$0.98 < ? < 1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find the right number together.

00:12 We're going to use the number line to figure out the possible numbers.

00:19 And there you have it! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Select a compatible number for the given range:

$0.98 < ? < 1$

Step-by-step solution

In order to discover our number range, we will first add zeros to the number 1 as follows:

$1=0.100$

This means our number will be in the range between 0.98 and 0.100

The numbers existing in this range are: $0.99$

Therefore, this is the correct answer.

Final Answer

$0.99$

Key Points to Remember

Essential concepts to master this topic

Inequality Rule: The symbol < means strictly less than, excluding boundary values
Technique: Find decimals between 0.98 and 1.00 like 0.99 or 0.995
Check: Verify 0.98 < 0.99 < 1.00 by comparing place values ✓

Common Mistakes

Avoid these frequent errors

Including the boundary values in the solution
Don't choose 0.98 or 1 as answers = these are boundary values that make the inequality false! The < symbol excludes these endpoints. Always pick numbers strictly between the boundaries, like 0.99.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can't I choose 0.98 or 1 as the answer?

The inequality uses < (strictly less than), not ≤. This means the number must be greater than 0.98 but less than 1, excluding both endpoints.

Are there other numbers that work besides 0.99?

Yes! Any decimal between 0.98 and 1 works: 0.981, 0.985, 0.99, 0.995, 0.999, etc. There are actually infinitely many correct answers!

How do I compare decimals to check if they're in the right range?

Compare place by place from left to right. For 0.99: it's greater than 0.98 (9 > 8 in hundredths place) and less than 1.00 (0.99 < 1.00).

What's the difference between < and ≤?

< means strictly less than (boundary not included), while ≤ means less than or equal (boundary included). Always check which symbol is used!

Can I write 1 as 1.00 to make comparison easier?

Absolutely! Adding zeros after the decimal point doesn't change the value: 1 = 1.0 = 1.00 = 1.000. This makes decimal comparisons much clearer.

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