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To convert \(4.082\) into a mixed number in its simplest form, let’s break it down:

1. **Separate the whole and decimal parts**: 
   - The whole number part of \(4.082\) is \(4\).
   - The decimal part is \(0.082\).

2. **Convert the decimal to a fraction**:
   - \(0.082\) can be written as \(\frac{82}{1000}\).

3. **Simplify the fraction**:
   - The fraction \(\frac{82}{1000}\) can be simplified by finding the greatest common divisor (GCD) of \(82\) and \(1000\), which is \(2\).
   - Dividing the numerator and the denominator by \(2\), we get:
     \[
     \frac{82 \div 2}{1000 \div 2} = \frac{41}{500}
     \]

4. **Combine the whole number and fraction**:
   - So, \(4.082\) as a mixed number in its simplest form is:
     \[
     4 \frac{41}{500}
     \]

The answer is **\(4 \frac{41}{500}\)**.

Would you like a more detailed explanation, or do you have any questions?

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### Related Questions:
1. How do you convert a decimal with three decimal places into a fraction?
2. What is the process for simplifying fractions?
3. Can you explain the concept of a mixed number?
4. How do you find the greatest common divisor (GCD) of two numbers?
5. Why is it important to express numbers in their simplest form?

### Tip:
When converting decimals to fractions, it’s helpful to identify how many decimal places are present to determine the denominator (e.g., three decimal places corresponds to a denominator of 1000).

Write 4.082 as a mixed number in its simplest form.

Learn how to convert the decimal 4.082 into a mixed number in its simplest form. This guide walks through the process of separating the whole number, converting the decimal part to a fraction, and simplifying using the greatest common divisor (GCD). Suitable for students in Grades 6-8.

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