Find a Number Between 0.46 and 0.49: Decimal Range Problem

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

The symbol means 'strictly less than' - the number cannot equal the boundary. The symbol ≤ means 'less than or equal to' - the boundary value would be included.

Q: How do I find numbers between 0.46 and 0.49?

Think of decimal place values! Numbers like $ 0.47 $ and $ 0.48 $ fall between these boundaries. You can also use three decimal places like 0.465 or 0.482.

Q: Why isn't 0.45 in the range?

Because \( 0.45 ! The number 0.45 is smaller than our lower boundary of 0.46, so it falls outside the range completely.

Q: Can I use 0.475 as an answer?

Absolutely! Any number between 0.46 and 0.49 works, including three-decimal numbers like 0.475, 0.463, or 0.488. The question asks for any compatible number in the range.

Q: How do I visualize this on a number line?

Draw a number line with 0.46 and 0.49 marked. Use open circles at both endpoints (since they're excluded) and shade the region between them. Any point in the shaded area works!

Decimal Inequalities with Number Line Ranges

Select a compatible number for the given range:

$0.46 < ? < 0.49$

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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

00:11 We'll choose the appropriate number from the options

00:14 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

Select a compatible number for the given range:

$0.46 < ? < 0.49$

Step-by-step solution

Let's look at our range of numbers and we'll see that our number is between 0.46 and 0.49

The numbers that exist in this range are: $0.47,\text{ }0.48$

Let's look at the answers and we'll see that 0.48 is within this range and therefore it is the correct answer

Final Answer

$0.48$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Number must be strictly between both boundary values
Technique: Check each option: 0.48 > 0.46 and 0.48 < 0.49 ✓
Verification: Boundary values 0.46 and 0.49 are excluded from the range ✓

Common Mistakes

Avoid these frequent errors

Including boundary values in the range
Don't think 0.46 or 0.49 work because they're 'close enough' = wrong answer! The symbols < mean strictly less than, not less than or equal to. Always exclude the exact boundary numbers from your range.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

What's the difference between < and ≤ symbols?

The symbol < means 'strictly less than' - the number cannot equal the boundary. The symbol ≤ means 'less than or equal to' - the boundary value would be included.

How do I find numbers between 0.46 and 0.49?

Think of decimal place values! Numbers like $0.47$ and $0.48$ fall between these boundaries. You can also use three decimal places like 0.465 or 0.482.

Why isn't 0.45 in the range?

Because $0.45 < 0.46$ ! The number 0.45 is smaller than our lower boundary of 0.46, so it falls outside the range completely.

Can I use 0.475 as an answer?

Absolutely! Any number between 0.46 and 0.49 works, including three-decimal numbers like 0.475, 0.463, or 0.488. The question asks for any compatible number in the range.

How do I visualize this on a number line?

Draw a number line with 0.46 and 0.49 marked. Use open circles at both endpoints (since they're excluded) and shade the region between them. Any point in the shaded area works!

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