Question

Example 9 : Show that 0.2353535... = 0.235 can be expressed in the form

where p and q are integers and q
not equal0.

​

Answer 1

SOLUTION

TO PROVE

0.2353535... can be expressed in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with $q \ne \: 0$

PROOF

Let $x = 0.2{ \overline{35}}$

⇒ x = 0.2353535... - - - - - - - (1)

Multiplying both sides by of (1) by 10 we get

⇒10x = 2.353535... - - - - - - (2)

Now Multiplying both sides of (1) by 1000 we get

⇒ 1000x = 235.353535... - - - - - (3)

Now Equation (3) - Equation (2) gives

$990x = 233$

$\implies \: \displaystyle \: x \: = \frac{233}{990}$

Which is of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p = 233 & q = 990 are integers with $q \ne \: 0$

Hence proved

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Answer 2

Answer:

233/990

Step-by-step explanation:

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