Solve the Decimal Inequality: Finding a Number Between 0.45 and 0.5

Q: How do I find a number between two decimals?

Look at the hundredths place! Since 0.45 has 5 hundredths and 0.50 has 0 hundredths (but represents 50), any number with 6, 7, 8, or 9 hundredths works: 0.46, 0.47, 0.48, 0.49.

Q: Why can't I choose 0.4 as the answer?

Because $ 0.4 = 0.40 $, which is less than 0.45! The number must be greater than 0.45, so 0.4 doesn't satisfy the first part of the inequality.

Q: Is 0.5 itself allowed in the answer?

No! The inequality uses $ (less than), not \( ≤ $ (less than or equal to). Your number must be strictly less than 0.5.

Q: What's the easiest way to check my answer?

Use the number line method: place 0.45, your answer, and 0.5 on a number line. Your answer should fall between the other two numbers when arranged in order.

Q: Can I use three decimal places like 0.475?

Yes! Any decimal between 0.45 and 0.5 works, whether it's 0.46, 0.475, 0.4823, etc. Just make sure it stays within the range.

Decimal Inequalities with Hundredths Precision

Fill in the compatible number:

$0.45 < ? < 0.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate number

00:07 It seems all these numbers are appropriate

00:17 Let's choose the appropriate number from the options

00:20 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 compatible number:

$0.45 < ? < 0.5$

Step-by-step solution

Let's add 0 to the number 0.5 to reveal the range between the two numbers:

$0.5=0.50$

In other words, the number should be between 45 and 50

Therefore, the appropriate answer is 0.48

Final Answer

$0.48$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Number must be greater than 0.45 and less than 0.5
Technique: Convert 0.5 to 0.50 to see hundredths clearly between 45-50
Check: Verify 0.45 < 0.48 < 0.50 by comparing each digit position ✓

Common Mistakes

Avoid these frequent errors

Choosing numbers outside the range
Don't pick 0.6 or 0.57 because they're greater than 0.5 = wrong range! Students often ignore the upper bound. Always check that your number satisfies both inequality conditions: greater than 0.45 AND less than 0.5.

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

How do I find a number between two decimals?

Look at the hundredths place! Since 0.45 has 5 hundredths and 0.50 has 0 hundredths (but represents 50), any number with 6, 7, 8, or 9 hundredths works: 0.46, 0.47, 0.48, 0.49.

Why can't I choose 0.4 as the answer?

Because $0.4 = 0.40$ , which is less than 0.45! The number must be greater than 0.45, so 0.4 doesn't satisfy the first part of the inequality.

Is 0.5 itself allowed in the answer?

No! The inequality uses $<$ (less than), not $≤$ (less than or equal to). Your number must be strictly less than 0.5.

What's the easiest way to check my answer?

Use the number line method: place 0.45, your answer, and 0.5 on a number line. Your answer should fall between the other two numbers when arranged in order.

Can I use three decimal places like 0.475?

Yes! Any decimal between 0.45 and 0.5 works, whether it's 0.46, 0.475, 0.4823, etc. Just make sure it stays within the range.

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