Feb 19, 2024
One way to demonstrate that 0.9 repeating equals 1 is through a mathematical approach. Consider the equation:
\[ x = 0.9\overline{9} \]
Multiply both sides of the equation by 10:
\[ 10x = 9.\overline{9} \]
Now, subtract the original equation from the multiplied one:
\[ 10x - x = 9.\overline{9} - 0.9\overline{9} \]
Simplify:
\[ 9x = 9 \]
Divide by 9:
\[ x = 1 \]
Therefore, \( 0.9\overline{9} = 1 \).
