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

Determine the numerical value of the shaded area:

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

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