Question

2. Show that 0.2353535... = 0.235 can be expressed in the form
, where p and q are integers
and q not equal to 0.
​

Answer 1

I hope it will help you

Answer 2

✯✯ QUESTION ✯✯

Show that 0.2353535 = 0.235 can be expressed in the form of p/q where p and q are integers and q is not equal to 0..

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✰✰ ANSWER ✰✰

$\longmapsto\tt{Let\:x=0.2353535....}$ ---- (1)

Multiply both sides by 100 : -

$\longmapsto\tt{100x=23.5353....}$ ---- (2)

Subtract Equation 1 from 2 : -

$\longmapsto\tt{100x-x=23.5353..-0.23535..}$

$\longmapsto\tt{99x=23.3}$

$\longmapsto\tt{99x=\dfrac{233}{10}}$

$\longmapsto\tt{99x\times{10}=233}$

$\longmapsto\tt{990x=233}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{\dfrac{233}{990}}}}$