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

Are they the same numbers?

$0.23\stackrel{?}{=}0.32$

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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