https://file.aiquickdraw.com/mathbot/file/1729795451358jwllff0w.jpg

To write \( 0.\overline{79} \) (which represents 0.797979... repeating) as a fraction, let's follow these steps:

### Step 1: Set up an equation
Let \( x = 0.\overline{79} \), meaning:
\[
x = 0.79797979\ldots
\]

### Step 2: Multiply both sides to eliminate the repeating decimal
Multiply both sides by 100 (since 79 is two digits) to shift the decimal point two places:
\[
100x = 79.79797979\ldots
\]

### Step 3: Subtract the two equations
Now, subtract the first equation from the second:
\[
100x - x = (79.797979\ldots) - (0.797979\ldots)
\]
This simplifies to:
\[
99x = 79
\]

### Step 4: Solve for \( x \)
Now, solve for \( x \) by dividing both sides by 99:
\[
x = \frac{79}{99}
\]

### Step 5: Simplify the fraction
The fraction \( \frac{79}{99} \) is already in its simplest form because 79 and 99 have no common factors other than 1.

Thus, \( 0.\overline{79} = \frac{79}{99} \).

Would you like further details or have any questions about this process?

Here are 5 related questions to explore:
1. How can you convert other repeating decimals like \( 0.\overline{56} \) into fractions?
2. What happens when the repeating part is only one digit (e.g., \( 0.\overline{3} \))?
3. Can non-repeating decimals be converted into fractions?
4. How can you verify the fraction form of a repeating decimal using long division?
5. What if the repeating decimal starts after some non-repeating digits (e.g., \( 0.123\overline{45} \))?

**Tip:** When converting repeating decimals into fractions, always count how many digits repeat and multiply the decimal by the appropriate power of 10 to eliminate the repeating part during subtraction.

Write 0.79 (with repeating 79) as a fraction.

Learn how to write 0.79 (repeating) as a fraction with a clear step-by-step solution. This method uses algebra to represent repeating decimals as rational numbers, making it suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation