Find the Decimal Between 0.1 and 0.2: Inequality Problem

Q: Why can't I choose 0.1 or 0.2 as my answer?

The inequality uses symbols, not ≤ (less than or equal to). This means your answer must be strictly between 0.1 and 0.2, so the endpoints are excluded.

Q: How many decimal numbers are between 0.1 and 0.2?

There are infinitely many decimal numbers between any two decimals! Some examples include: $ 0.11, 0.125, 0.15, 0.175, 0.19 $, and many more.

Q: Why does the explanation add zeros to make 0.10 and 0.20?

Adding zeros helps you visualize the range better! When both numbers have the same decimal places, it's easier to see which numbers fit between them.

Q: Can I pick any number between 0.1 and 0.2?

Yes! Any decimal strictly between these values works. From the given choices, only $ 0.15 $ satisfies \( 0.1 .

Q: What if the inequality used ≤ instead of <?

If it used ≤ (less than or equal to), then the boundary values 0.1 and 0.2 would be valid answers. Always pay attention to whether the inequality is strict (

Decimal Inequalities with Range Finding

Fill in the missing number (?):

$0.1 < ? < 0.2$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate number

00:03 We'll use the number line to find the possible numbers

00:18 We can see that all these numbers fit

00:23 We'll choose the appropriate number from the options

00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing number (?):

$0.1 < ? < 0.2$

Step-by-step solution

In order to discover our number range, we will first add 0 to both numbers as follows:

$0.1=0.10$

$0.2=0.20$

This means our number will be in the range of 0.10 to 0.20.

The numbers that exist in this range are: $0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19$

Now if we look at the possible answers, we can see that 0.15 is within this range and therefore is the correct answer.

Final Answer

$0.15$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Numbers between 0.1 and 0.2 exclude the endpoints
Technique: Convert to 0.10 < ? < 0.20 for easier visualization
Check: Verify 0.15 is greater than 0.10 and less than 0.20 ✓

Common Mistakes

Avoid these frequent errors

Including the boundary values as valid answers
Don't choose 0.1 or 0.2 as answers since the inequality uses < not ≤! The symbols mean "strictly less than," so boundary values don't work. Always check that your answer is truly between the given values, not equal to them.

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 0.1 or 0.2 as my answer?

The inequality uses < (less than) symbols, not ≤ (less than or equal to). This means your answer must be strictly between 0.1 and 0.2, so the endpoints are excluded.

How many decimal numbers are between 0.1 and 0.2?

There are infinitely many decimal numbers between any two decimals! Some examples include: $0.11, 0.125, 0.15, 0.175, 0.19$ , and many more.

Why does the explanation add zeros to make 0.10 and 0.20?

Adding zeros helps you visualize the range better! When both numbers have the same decimal places, it's easier to see which numbers fit between them.

Can I pick any number between 0.1 and 0.2?

Yes! Any decimal strictly between these values works. From the given choices, only $0.15$ satisfies $0.1 < 0.15 < 0.2$ .

What if the inequality used ≤ instead of +

If it used ≤ (less than or equal to), then the boundary values 0.1 and 0.2 would be valid answers. Always pay attention to whether the inequality is strict (<) or inclusive (≤)!

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