Question

express 0.282828.....in the form p/q , wher p and q are Integers but q not equal to 0​

Answer 1

let x = 0.282828........

10 x = 28.282828.......

by subtracting :

9x = 28

x = 28 / 9

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Answer 2

Concept: In mathematics, any number that can be written as p/q where q 0 is considered a rational number. Additionally, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers. The outcome of dividing a rational number, or fraction, will be a decimal number, either a terminating decimal or a repeating decimal.

Given: 0.282828.....

To find: the p/q form of 0.282828....

Solution: Let x = 0.282828...... ------ (i)

               Multiplying equation (i) by 100

               100x = 28.282828..... ----- (ii)

Now, subtracting equation eqn (i) from eqn (ii),

100x = 28.282828....

-      x = 0.282828......

we get

99x = 28

$x = \frac{28}{99}$

Hence, the value of x is 28/99.

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