Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Transcription for Educational Website:
---
**Convert .\overline{4} to a Fraction**
To change the repeating decimal .4 (where 4 is repeating) into a fraction, follow the steps below:
1. Let \( x = 0.4444\ldots \)
2. Multiply both sides by 10 to shift the decimal: \( 10x = 4.4444\ldots \)
3. Subtract the original equation from this new equation:
\[
10x - x = 4.4444\ldots - 0.4444\ldots
\]
\[
9x = 4
\]
4. Solve for \( x \) by dividing both sides by 9:
\[
x = \frac{4}{9}
\]
**Solution:**
The repeating decimal \( .\overline{4} \) can be expressed as the fraction \( \frac{4}{9} \).
---
In the image:
- You'll see the question "Change .4 to a fraction."
- Below the text, there is a placeholder for the fraction with "4" over an empty box labeled "[?]".
This setup indicates that users should determine the denominator of the fraction that converts the repeating decimal to a fraction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58531ebd-4d7b-4587-924e-328516ceeabd%2Fb5d831e7-d9a6-4845-9fbe-dfd17f2302c0%2Fcskqjsw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Transcription for Educational Website:
---
**Convert .\overline{4} to a Fraction**
To change the repeating decimal .4 (where 4 is repeating) into a fraction, follow the steps below:
1. Let \( x = 0.4444\ldots \)
2. Multiply both sides by 10 to shift the decimal: \( 10x = 4.4444\ldots \)
3. Subtract the original equation from this new equation:
\[
10x - x = 4.4444\ldots - 0.4444\ldots
\]
\[
9x = 4
\]
4. Solve for \( x \) by dividing both sides by 9:
\[
x = \frac{4}{9}
\]
**Solution:**
The repeating decimal \( .\overline{4} \) can be expressed as the fraction \( \frac{4}{9} \).
---
In the image:
- You'll see the question "Change .4 to a fraction."
- Below the text, there is a placeholder for the fraction with "4" over an empty box labeled "[?]".
This setup indicates that users should determine the denominator of the fraction that converts the repeating decimal to a fraction.
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