https://file.aiquickdraw.com/mathbot/file/1726699202867c45gan7q.jpg

Let's work through part (c) where we need to express the repeating decimal \( 2.\overline{715} \) as a fraction.

### Steps to convert a repeating decimal to a fraction:

Let \( x = 2.\overline{715} \), meaning:
\[ x = 2.715715715\ldots \]

#### Step 1: Eliminate the repeating part by multiplying both sides by 1000.
This shifts the decimal point three places:
\[
1000x = 2715.715715715\ldots
\]

#### Step 2: Subtract the original \( x = 2.715715715\ldots \) from the equation.
\[
1000x - x = 2715.715715715\ldots - 2.715715715\ldots
\]
\[
999x = 2713
\]

#### Step 3: Solve for \( x \):
\[
x = \frac{2713}{999}
\]

#### Step 4: Simplify the fraction (if possible).
We now check if \( \frac{2713}{999} \) can be simplified. However, 2713 and 999 have no common factors, so the fraction is already in its simplest form.

Thus, the repeating decimal \( 2.\overline{715} \) as a fraction is:
\[
\boxed{\frac{2713}{999}}
\]

Let me know if you need more details or have any other questions!

Here are five related questions to expand on this:
1. How do you convert a non-repeating decimal to a fraction?
2. What is the general method to convert any repeating decimal to a fraction?
3. Why is it important to simplify fractions?
4. Can repeating decimals always be expressed as fractions?
5. What are some real-world applications of converting repeating decimals to fractions?

**Tip:** When simplifying fractions, always check for the greatest common divisor (GCD) of the numerator and denominator to ensure the fraction is in its simplest form.

Express the repeating decimal 2.715 (with 715 repeating) as a fraction.

This page explains how to express the repeating decimal 2.715 (with 715 repeating) as a fraction. Step-by-step instructions using algebraic methods, including how to eliminate the repeating decimal, solve for x, and simplify the fraction. Suitable for students in Grades 8-10.

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