Chapter 1: Number Systems

Let x = 0.6

Multiply by 10 on L.H.S and R.H.S,

10x = 6

x = 6/10

x = 3/5

So, the p/q form of 0.6 = 3/5

Let y = 0.77777…

Multiply by 10 on L.H.S and R.H.S,

10y = 7.7777…

10y – y = 7.7777777……. – 0.7777777…………..

9y = 7

y = 7/9

So the p/q form of 0.7777… = 7/9

Let z = 0.47777…

Multiply by 10 on L.H.S and R.H.S,

10z = 4.7777…

10z – z = 4.7777777… – 0.47777777…

9z = 4.2999

z ≈ 4.3/9

z = 43/90

So the p/q form of  0.4777… = 43/90

Therefore, p/q form of

is,

x+y+z = 3/5 + 7/9 + 43/90

= (54 + 70 + 43)/90

= 167/90

Let us first make the denominators the same,

To make the denominators the same, cross-multiply the first and second terms of the equation.

Now, again make the denominators the same by cross-multiplying the obtained term and the third term of the given equation in the question.

Let us first make the denominators the same by cross multiplication method

Observing the denominator, we can say that,

Denominators are of the form,

(a + b) × (a – b) = (a² – b²)

Here a = 3√3

b = 2√2

a² = (3√3)² = 27

b² = (2√2)² = 8