Question

Express 0.47(bar on 7)in the form of p/q where p and q are integers an q is not equal to 0

Answer 1

Let x= 0.47 (bar on 7)

Multiplying sides by 10

10x=4.7(bar on 7)-l

Multiplying both sides by 10

100x=47.7-ll

Now, subtract ll-l

100x-10x = 47.7-4.7

90x=430

x= 430/90

x=4.7

Answer 2

p/q form of 0.47(bar on 7) is 43/90

Given:

Irrational number 0.47(bar on 7)

To Find:

Express 0.47(bar on 7)in the form of p/q

Solution:

Given 0.47(bar on 7) = 0.477777....

To change the given number into p/q form follow the following method

Let x = 0.477777.... ----(1)

Multiply (1) with 100

⇒ 10x = 47.7777 ....-----(2)

Subtract (1) from (2)

⇒ 10x - x = 4.77777 - 0.477777

⇒ 9x = 4.3  

⇒ x = 4.3/9

Here, p is still as irrational number

So multiply and divide 4.3/9 by 10

⇒ $(\frac{4.3}{9} )\frac{10}{10}$ = $\frac{43}{90}$

Therefore,

p/q form of 0.47(bar on 7) is 43/90

#SPJ2