Solve the Double Inequality: Finding a Number Between 0.47 and 0.5

Q: Why do we write 0.5 as 0.50?

Writing $ 0.5 = 0.50 $ helps you compare hundredths places directly! Now you can easily see that numbers like 0.48 and 0.49 fit between 0.47 and 0.50.

Q: How many numbers can fit between 0.47 and 0.5?

Looking at hundredths, only 0.48 and 0.49 fit! But if we consider thousandths like 0.471, 0.472, 0.473... there are infinitely many decimal numbers in this range.

Q: What if I picked 0.46 instead of 0.48?

Check both parts: Is \( 0.47 ? No! Since 0.46 is less than 0.47, it doesn't satisfy the first part of the inequality.

Q: How do I remember which way the inequality signs point?

The open side of always points to the larger number! In \( 0.47 , both signs open toward the missing number, meaning it's larger than 0.47 but smaller than 0.5.

Q: Can I use a number line to help solve this?

Absolutely! Draw a number line and mark 0.47 and 0.50. Your answer must fall in the open interval between these two points (not including the endpoints).

Double Inequalities with Decimal Numbers

What is the missing number?

$0.47 < ? < 0.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the appropriate number

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

00:18 We can see that all these numbers are suitable

00:21 Let's choose the appropriate number from the options

00:24 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?

$0.47 < ? < 0.5$

Step-by-step solution

To work out the range of numbers, we will add 0 to the number 0.5 as follows:

$0.5=0.50$

In other words, our number should be between $0.47$ and $0.50$ .

The numbers that exist within this range are $0.48$ and $0.49$ .

Looking at the options, we can see that the only possible 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 0.47 AND less than 0.50
Technique: Convert 0.5 to 0.50 to compare hundredths place clearly
Check: Verify 0.47 < 0.48 < 0.50 by comparing each digit ✓

Common Mistakes

Avoid these frequent errors

Choosing numbers outside the range
Don't pick 0.46 or 0.52 just because they're close = wrong answer! These numbers don't satisfy both parts of the inequality. Always check that your number is greater than the left value AND less than the right value.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why do we write 0.5 as 0.50?

Writing $0.5 = 0.50$ helps you compare hundredths places directly! Now you can easily see that numbers like 0.48 and 0.49 fit between 0.47 and 0.50.

How many numbers can fit between 0.47 and 0.5?

Looking at hundredths, only 0.48 and 0.49 fit! But if we consider thousandths like 0.471, 0.472, 0.473... there are infinitely many decimal numbers in this range.

What if I picked 0.46 instead of 0.48?

Check both parts: Is $0.47 < 0.46$ ? No! Since 0.46 is less than 0.47, it doesn't satisfy the first part of the inequality.

How do I remember which way the inequality signs point?

The open side of < or > always points to the larger number! In $0.47 < ? < 0.5$ , both signs open toward the missing number, meaning it's larger than 0.47 but smaller than 0.5.

Can I use a number line to help solve this?

Absolutely! Draw a number line and mark 0.47 and 0.50. Your answer must fall in the open interval between these two points (not including the endpoints).

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