Answer: \(1.\bar{21}=\frac{40}{33}\)
Step-by-step explanation:
Since we have given that
\(1.\bar{21}\)
Let x = \(1.\bar{21}\) --------------(1)
Multiplying by 100 on both the sides:
\(100x=121.\bar{21}---------------(2)\)
Subtracting (1) from (2), we get,
\(100x-x=121.\bar{21}-1.\bar{21}\\\\99x=120\\\\x=\frac{120}{99}\\\\x=\frac{40}{33}\)
Hence, \(1.\bar{21}=\frac{40}{33}\)
