Question
Is 0.22222… a repeating decimal
Answers
Answer
How about 8.44444…
Answered by
GPT-4o mini
Yes, \(0.22222...\) is a repeating decimal. It can also be represented more concisely as \(0.\overline{2}\), where the bar indicates that the digit 2 repeats indefinitely. Repeating decimals can be expressed as fractions; in this case, \(0.22222...\) is equal to \(\frac{2}{9}\).
Answered by
GPT-4o mini
Yes, \(8.44444...\) is also a repeating decimal. It can be expressed as \(8.4\overline{4}\), where the bar indicates that the digit 4 repeats indefinitely after the decimal point.
This repeating decimal can be converted to a fraction. To do this, let \(x = 8.44444...\). Then, you can manipulate the equation as follows:
1. Multiply both sides by 10 to shift the decimal point:
\[
10x = 84.44444...
\]
2. Now, subtract the original \(x\) from this equation:
\[
10x - x = 84.44444... - 8.44444...
\]
This simplifies to:
\[
9x = 76
\]
3. Divide by 9:
\[
x = \frac{76}{9}
\]
Thus, \(8.44444...\) is equal to the fraction \(\frac{76}{9}\).
This repeating decimal can be converted to a fraction. To do this, let \(x = 8.44444...\). Then, you can manipulate the equation as follows:
1. Multiply both sides by 10 to shift the decimal point:
\[
10x = 84.44444...
\]
2. Now, subtract the original \(x\) from this equation:
\[
10x - x = 84.44444... - 8.44444...
\]
This simplifies to:
\[
9x = 76
\]
3. Divide by 9:
\[
x = \frac{76}{9}
\]
Thus, \(8.44444...\) is equal to the fraction \(\frac{76}{9}\).