Question

show that 0.3333...= 0.3 can be expressed in the form p/q where p and q are integer and q ≠ 0...​

Answer 1

$\huge \sf \red{ \underline{Solution:-}}$

• since, we don't know what 0.3 is, let us call it ‘x' and so,

⠀⠀⠀⠀⠀⠀⠀x = 0.3333...

⠀_______________________

Now, here is where the trick comes in. look at:-

• Now,

$\sf \implies\green{10x = 10 \times (0.333...) = 3.333}$

$\sf \implies \pink{3.3333... = 3, + x \: since \: x = 0.3333....}$

⠀⠀⠀⠀⠀$\sf\implies\green{10x = 3 + x}$

⠀_______________________

⠀⠀⠀⠀solving for “x”, we get:-

⠀⠀⠀⠀⠀⠀9x = 3,i.e., x =1/3

⠀_______________________

Answer 2

$\huge \sf \red{ \underline{‘Solution’}}$

• since, we don't know what 0.3 is, let us call it ‘x' and so,

$\sf \to \pink{x = 0.3333...}$

Now, here is where the trick comes in. look at

• Now,

$\bf \implies \orange{10x = 10 \times (0.333...) = 3.333}$

$\bf \implies \pink{3.3333... = 3 + x \: since \: x = 0.3333....}$

$\bf \implies \orange{10x = 3 + x}$

• solving for “x”, we get,

$\sf \to \purple{ \underline{9x = 3 \: i.e. \: x = \frac{1}{3}}}$