Arrange Digits 2,0,7,5: Finding the Smallest Possible Decimal

Q: Why can't I put 0 in the tenths place?

Because 0 in tenths place creates 0.0275, which uses 5 digits total instead of the required 4 digits. We must use exactly the given digits: 2, 0, 7, 5.

Q: How do I know which digit goes in tenths place?

Choose the smallest non-zero digit for tenths place to make the decimal as small as possible. Since we have 2, 0, 7, 5, the digit 2 goes in tenths place.

Q: What if I want the largest decimal instead?

For the largest decimal, put the largest digit in tenths place first: 0.752. Then arrange remaining digits in descending order.

Q: Why does 0.257 beat 0.275?

Compare digit by digit from left to right. Both start 0.2__, but in hundredths place: 5 , so 0.257 is smaller than 0.275.

Q: Can I make a whole number instead?

Yes! You could make 2057, but the question asks for a decimal. Since 0.257

Decimal Formation with Digit Arrangement

Form the smallest possible decimal using the digits below:

$2,0,7,5$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Form the smallest possible decimal using the digits below:

$2,0,7,5$

Step-by-step solution

To solve this problem, we follow these steps:

Step 1: Identify the smallest non-zero digit to place in the tenths position. Here, that digit is 2.
Step 2: Place 0 in the integer position to ensure the number is less than one.
Step 3: Arrange the remaining digits, 7 and 5, in ascending order after the tenths position.

Implementation of these steps:
- The smallest digit 2 goes in the tenths place.
- 0 is used as the integer part to remain less than 1, resulting in $0.2$ .

Continue arranging the remaining digits:
The digits 5 and 7 go next, resulting in 0.257.

This gives us the smallest possible decimal using the digits: 0.257.

Final Answer

0.257

Key Points to Remember

Essential concepts to master this topic

Rule: Place smallest non-zero digit in tenths place first
Technique: Use 0 in ones place: 0.2__ is smaller than 2.0__
Check: Compare decimal values: 0.257 < 0.275 < 0.527 < 0.572 ✓

Common Mistakes

Avoid these frequent errors

Placing 0 in the tenths position
Don't put 0 right after the decimal point like 0.0275 = using extra digits! This creates a completely different number with more decimal places. Always place 0 in the ones position and start with the smallest non-zero digit in tenths place.

Practice Quiz

Test your knowledge with interactive questions

Which figure represents 0.1?

FAQ

Everything you need to know about this question

Why can't I put 0 in the tenths place?

Because 0 in tenths place creates 0.0275, which uses 5 digits total instead of the required 4 digits. We must use exactly the given digits: 2, 0, 7, 5.

How do I know which digit goes in tenths place?

Choose the smallest non-zero digit for tenths place to make the decimal as small as possible. Since we have 2, 0, 7, 5, the digit 2 goes in tenths place.

What if I want the largest decimal instead?

For the largest decimal, put the largest digit in tenths place first: 0.752. Then arrange remaining digits in descending order.

Why does 0.257 beat 0.275?

Compare digit by digit from left to right. Both start 0.2__, but in hundredths place: 5 < 7, so 0.257 is smaller than 0.275.

Can I make a whole number instead?

Yes! You could make 2057, but the question asks for a decimal. Since 0.257 < 2057, the decimal form gives us the truly smallest possible number.

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