Question
convert 0.8 to a rational number ( 8 is repeated)
Answers
GPT-4o mini
To convert the repeating decimal \(0.888...\) (where 8 repeats) into a rational number, you can follow these steps:
1. Let \(x = 0.888...\).
2. Multiply both sides by 10 to shift the decimal point:
\(10x = 8.888...\).
3. Now, you have two equations:
- \(x = 0.888...\)
- \(10x = 8.888...\)
4. Subtract the first equation from the second:
\(10x - x = 8.888... - 0.888...\)
\(9x = 8\)
5. Solve for \(x\):
\(x = \frac{8}{9}\)
Thus, the repeating decimal \(0.888...\) can be expressed as the rational number \(\frac{8}{9}\).
1. Let \(x = 0.888...\).
2. Multiply both sides by 10 to shift the decimal point:
\(10x = 8.888...\).
3. Now, you have two equations:
- \(x = 0.888...\)
- \(10x = 8.888...\)
4. Subtract the first equation from the second:
\(10x - x = 8.888... - 0.888...\)
\(9x = 8\)
5. Solve for \(x\):
\(x = \frac{8}{9}\)
Thus, the repeating decimal \(0.888...\) can be expressed as the rational number \(\frac{8}{9}\).