Arrange Digits 2,0,7,4 to Create Decimal Closest to 1/2

Q: Why do I need to check all possible arrangements of the digits?

Different arrangements create completely different decimal values! For example, using digits 2,0,7,4: 0.274 ≠ 0.472. Each arrangement could be the closest to $ \frac{1}{2} $, so you must test them all.

Q: How do I calculate the distance between two decimals?

Use absolute difference: $ |a - b| $. For example: $ |0.472 - 0.5| = |−0.028| = 0.028 $. The absolute value ensures distance is always positive.

Q: Can I use mental math to estimate which decimal is closest?

Yes, but be careful! 0.5 is halfway between 0 and 1. Look for decimals close to 0.5. But always calculate exact distances to be sure - sometimes close estimates can fool you!

Q: What if I can't use all the given digits?

You must use each digit exactly once - that's the rule! If you have digits 2,0,7,4, every arrangement must contain all four digits in some order as a three-decimal-place number.

Q: Why is 0.472 better than 0.427 when they look similar?

Calculate the distances: $ |0.472 - 0.5| = 0.028 $ vs $ |0.427 - 0.5| = 0.073 $. Even though both are close to 0.5, 0.472 is actually much closer!

Q: Do I need to consider arrangements like 2.074 or 20.74?

No! The question asks for decimals closest to $ \frac{1}{2} = 0.5 $. Numbers like 2.074 are much larger than 0.5, so focus on arrangements that start with 0.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Using the digits, compose the number closest to half

00:03 Let's write all possible options

00:22 Let's compare to half

00:32 Let's draw a number line and plot the numbers

01:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Using the digits below (only once per digit)

$2,0,7,4$

Form the decimal which is closest in value to one half :

2

Step-by-step solution

To solve this problem, we'll examine the combinations and their proximity to 0.5:

Step 1: Identify the available digits: 2, 0,7, and 4.
Step 2: Form potential decimals: 0.742, 0.274, 0.427, 0.472.
Step 3: Calculate the distance between each number and 0.5.

Now, let's work through each step:

Step 1: Available Digits
We need to use each digit 2, 0, 7, and 4 exactly once to form a decimal number.

Step 2: Potential Combinations
- $0.742$
- $0.274$
- $0.427$
- $0.472$

Step 3: Calculate and Compare
We need to compare each decimal to 0.5:
- Difference between $0.742$ and $0.5$ is $0.742 - 0.5 = 0.242$
- Difference between $0.274$ and $0.5$ is $0.5 - 0.274 = 0.226$
- Difference between $0.427$ and $0.5$ is $0.5 - 0.427 = 0.073$
- Difference between $0.472$ and $0.5$ is $0.5 - 0.472 = 0.028$

On comparing these differences, $0.472$ has the smallest difference from $0.5$ . Therefore, 0.472 is the decimal number closest to one half.

Therefore, the solution to the problem is 0.472.

3

Final Answer

0.472

Key Points to Remember

Essential concepts to master this topic

Strategy: Arrange digits to minimize distance from target value
Technique: Calculate $|decimal - 0.5|$ for each arrangement
Check: Verify $|0.472 - 0.5| = 0.028$ is smallest difference ✓

Common Mistakes

Avoid these frequent errors

Comparing decimal values directly without calculating distances
Don't just look at which decimal is "bigger" or "smaller" than 0.5 = wrong comparison! You need the actual distance. Always calculate the absolute difference $|decimal - 0.5|$ for each arrangement to find the closest value.

Practice Quiz

Test your knowledge with interactive questions

Which figure represents 0.1?

FAQ

Everything you need to know about this question

Why do I need to check all possible arrangements of the digits?

+

Different arrangements create completely different decimal values! For example, using digits 2,0,7,4: 0.274 ≠ 0.472. Each arrangement could be the closest to $\frac{1}{2}$ , so you must test them all.

How do I calculate the distance between two decimals?

+

Use absolute difference: $|a - b|$ . For example: $|0.472 - 0.5| = |−0.028| = 0.028$ . The absolute value ensures distance is always positive.

Can I use mental math to estimate which decimal is closest?

+

Yes, but be careful! 0.5 is halfway between 0 and 1. Look for decimals close to 0.5. But always calculate exact distances to be sure - sometimes close estimates can fool you!

What if I can't use all the given digits?

+

You must use each digit exactly once - that's the rule! If you have digits 2,0,7,4, every arrangement must contain all four digits in some order as a three-decimal-place number.

Why is 0.472 better than 0.427 when they look similar?

+

Calculate the distances: $|0.472 - 0.5| = 0.028$ vs $|0.427 - 0.5| = 0.073$ . Even though both are close to 0.5, 0.472 is actually much closer!

Do I need to consider arrangements like 2.074 or 20.74?

+

No! The question asks for decimals closest to $\frac{1}{2} = 0.5$ . Numbers like 2.074 are much larger than 0.5, so focus on arrangements that start with 0.

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Arrange Digits 2,0,7,4 to Create Decimal Closest to 1/2

Decimal Arrangement with Distance Optimization

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