Question

What is 1.21 repeating as a fraction?

Answer 1

$x=1.\overline{21}\\ 100x=121.\overline{21}\\ 100x-x=121.\overline{21}-1.\overline{21}\\ 99x=120\\ x=\dfrac{120}{99}=\dfrac{40}{33}$

Answer 2

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, $1.\bar{21}=\frac{40}{33}$