Use the repeating decimal 8.3¯
.

Part A

How can it be represented as a mixed number?
	8
13
	8
310
	8
23
	8
38

Part B

How can it be represented as an improper fraction?
	253
	8310
	263
	698

### Part A: Converting the Repeating Decimal \( 8.\overline{3} \) to a Mixed Number

The repeating decimal \( 8.\overline{3} \) can be rewritten as \( 8 + 0.\overline{3} \). 

To convert \( 0.\overline{3} \) into a fraction:

1. Let \( x = 0.\overline{3} \).
2. Multiply both sides by 10 to eliminate the repeating part:  
   \( 10x = 3.\overline{3} \).
3. Subtract the original \( x \) from this new equation:  
   \( 10x - x = 3.\overline{3} - 0.\overline{3} \).  
   This simplifies to:  
   \( 9x = 3 \).
4. Solving for \( x \), we get:  
   \( x = \frac{3}{9} = \frac{1}{3} \).

So, \( 8.\overline{3} = 8 + \frac{1}{3} \). Therefore, the mixed number representation is:

**Answer for Part A: \( 8 \frac{1}{3} \)**.

Among the given options, \( 8 \frac{1}{3} \) matches this answer.

### Part B: Converting \( 8 \frac{1}{3} \) to an Improper Fraction

To convert the mixed number \( 8 \frac{1}{3} \) to an improper fraction:

1. Multiply the whole number by the denominator:  
   \( 8 \times 3 = 24 \).
2. Add the numerator:  
   \( 24 + 1 = 25 \).
3. Place the result over the original denominator:  
   \( \frac{25}{3} \).

**Answer for Part B: \( \frac{25}{3} \)**.

Among the given options, \( \frac{25}{3} \) matches this answer.

### Summary:
- **Part A Answer**: \( 8 \frac{1}{3} \)
- **Part B Answer**: \( \frac{25}{3} \)

Would you like a detailed explanation of any of these steps, or do you have any further questions?

### Related Questions:
1. How do you convert repeating decimals with two repeating digits to fractions?
2. How can mixed numbers be converted back into decimals?
3. What are the steps to simplify fractions?
4. How can you determine if a fraction is in its simplest form?
5. What are the properties of repeating decimals?

**Tip:** Always double-check your calculations, especially when converting repeating decimals to fractions, as small errors can lead to incorrect results.

Use the repeating decimal 8.3¯. Part A: How can it be represented as a mixed number? Options: 8 1/3, 8 10/3, 8 2/3, 8 3/8. Part B: How can it be represented as an improper fraction? Options: 25/3, 8/10, 26/3, 6/98.

Learn how to convert the repeating decimal 8.3¯ to its mixed number and improper fraction representations. This problem involves basic arithmetic operations, including converting repeating decimals to fractions and mixed numbers to improper fractions. Suitable for students in Grades 6-8.

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