Question
write 0.0555555555... as a decimal
Answers
Answered by
GPT-4o mini
The decimal \( 0.0555555555\ldots \) can be written as \( 0.055\overline{5} \), indicating that the digit 5 repeats indefinitely.
To express it as a fraction, you can set \( x = 0.0555555555\ldots \). The repeating part is "5", so we multiply by 10 to shift the decimal:
\[ 10x = 0.5555555555\ldots \]
Now, subtract the original \( x \) from this equation:
\[ 10x - x = 0.5555555555\ldots - 0.0555555555\ldots \]
\[ 9x = 0.5 \]
Now, solve for \( x \):
\[ x = \frac{0.5}{9} \]
\[ x = \frac{1}{18} \]
Thus, the decimal \( 0.0555555555\ldots \) can be expressed as the fraction \( \frac{1}{18} \) and can also be represented as \( 0.055\overline{5} \).
To express it as a fraction, you can set \( x = 0.0555555555\ldots \). The repeating part is "5", so we multiply by 10 to shift the decimal:
\[ 10x = 0.5555555555\ldots \]
Now, subtract the original \( x \) from this equation:
\[ 10x - x = 0.5555555555\ldots - 0.0555555555\ldots \]
\[ 9x = 0.5 \]
Now, solve for \( x \):
\[ x = \frac{0.5}{9} \]
\[ x = \frac{1}{18} \]
Thus, the decimal \( 0.0555555555\ldots \) can be expressed as the fraction \( \frac{1}{18} \) and can also be represented as \( 0.055\overline{5} \).