Question

Q2. Express 0.344444.........-0.2 +0.66666..... in the form of​

Answer 1

Your question is incomplete

Complete question : 0.3444.. - 0.2 + 0.66.. in the form of p/q

First we need to express all terms in p/q form

Consider 0.344..

Let x = 0.344.. --(1)

Here periodicity = 1

So, multiply (1) with 10

10 * x = 10 * 0.344..

10x = 3.44.. ---(2)

Subtract (1) from (2)

10x = 3.444...

-x = 0.344...

_________________

9x = 3.1

_________________

$x = \dfrac{3.1 \times 10}{9 \times 10} \\ \\ x = \frac{31}{90}$

So, p/q form of 0.3444.. is 31/90

__________________________________

Consider - 0.2

$- 0.2 = - \dfrac{0.2 \times 10}{1 \times 10} \\ \\ - 0.2 = - \dfrac{2}{10}$

So, p/q form of -0.2 is -2/10

__________________________________

Consider 0.666....

Let x = 0.66.... --(1)

Here periodicity = 1

So, multiply (1) with 10

10 * x = 10 * 0.666..

10x = 6.666... ---(2)

Subtract (1) from (2)

10x = 6.666...

-x = 0.666...

_________________

9x = 6

_________________

$x = \dfrac{6}{9}$

So, p/q form of 0.66.. is 6/9

__________________________________

Now consider 0.3444.. - 0.2 + 0.66..

You need to substitute the respective form in the above statement.

$0.344.. -0.2 + 0.666.. = \dfrac{31}{9} - \dfrac{2}{10} + \dfrac{6}{9}$

Before adding we need to make all the denominator same. To do that find the Least Common Multiple of 9, 10, 90

So, Least Common Multiple of 9, 10, 90 = 90

Now multiply numerators and denominators to with appropriate numbers such that denominator will become same i.e, make the unlike fractions as like fractions

$= \dfrac{31}{90} - \dfrac{2 \times 9}{10 \times 9} + \dfrac{6 \times 10}{9 \times 10}$

$= \dfrac{31}{90} - \dfrac{18}{90} + \frac{60}{90}$

Now you can add

$= \dfrac{31 + 60}{90} - \dfrac{18}{90}$

$= \dfrac{91}{90} - \dfrac{18}{90}$

$= \dfrac{91 - 18}{90}$

$= \dfrac{73}{90}$

So, 0.3444.. - 0.2 + 0.66.. in the form of p/q is 73/90.

_________________________________