Find the Decimal Between 0.2 and 0.3: Inequality Problem

Q: Why can't 0.2 or 0.3 be the answer?

The inequality uses < symbols, which means strictly less than. Since we need a number greater than 0.2 AND less than 0.3, the endpoints 0.2 and 0.3 themselves don't qualify.

Q: How do I find all possible numbers in this range?

Convert both bounds to the same decimal places: $ 0.2 = 0.20 $ and $ 0.3 = 0.30 $. Then list all hundredths between them: 0.21, 0.22, 0.23... 0.29.

Q: Is 0.25 also a correct answer?

Yes! Any decimal between 0.2 and 0.3 would be mathematically correct. However, you must choose from the given options in multiple choice questions. Among the choices, only 0.28 fits the range.

Q: What if I need to compare more complex decimals?

Always line up decimal points and compare digit by digit from left to right. Add zeros as needed: 0.2 becomes 0.20, making it easier to see that 0.25 > 0.20.

Q: How can I quickly check if my answer is right?

Use the number line method: place 0.2, your answer, and 0.3 on a line. Your number should be physically between the other two. If not, it's wrong!

Decimal Inequalities with Number Range Analysis

What is the missing number number?

$0.2 < ? < 0.3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate number

00:04 We'll use the number line to find the possible numbers

00:23 We can see that all these numbers fit

00:28 Let's choose the appropriate number from the options

00:31 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

What is the missing number number?

$0.2 < ? < 0.3$

Step-by-step solution

To find out which numbers appear in our number range, we will first add 0 to both numbers as follows:

$0.2=\text{0}.20$

$0.3=0.30$

This means that our number is between 0.20 and 0.30.

The numbers existing in this range are: $0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,$ and $0.29$ .

Looking at the possible answers, we can see that 0.28 must be the correct one.

Final Answer

$0.28$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert decimals to same place value for easier comparison
Technique: List all hundredths: 0.21, 0.22, 0.23... 0.29 between bounds
Check: Verify 0.20 < 0.28 < 0.30 by comparing place values ✓

Common Mistakes

Avoid these frequent errors

Choosing numbers outside the given range
Don't pick 0.18 or 0.38 without checking if they fit = wrong answer! These numbers fall outside our bounds of 0.2 to 0.3. Always verify your choice satisfies both inequality conditions before selecting.

Practice Quiz

Test your knowledge with interactive questions

Are they the same numbers?

$0.1\stackrel{?}{=}0.10$

FAQ

Everything you need to know about this question

Why can't 0.2 or 0.3 be the answer?

The inequality uses < symbols, which means strictly less than. Since we need a number greater than 0.2 AND less than 0.3, the endpoints 0.2 and 0.3 themselves don't qualify.

How do I find all possible numbers in this range?

Convert both bounds to the same decimal places: $0.2 = 0.20$ and $0.3 = 0.30$ . Then list all hundredths between them: 0.21, 0.22, 0.23... 0.29.

Is 0.25 also a correct answer?

Yes! Any decimal between 0.2 and 0.3 would be mathematically correct. However, you must choose from the given options in multiple choice questions. Among the choices, only 0.28 fits the range.

What if I need to compare more complex decimals?

Always line up decimal points and compare digit by digit from left to right. Add zeros as needed: 0.2 becomes 0.20, making it easier to see that 0.25 > 0.20.

How can I quickly check if my answer is right?

Use the number line method: place 0.2, your answer, and 0.3 on a line. Your number should be physically between the other two. If not, it's wrong!

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