Question

Express in the form of p/q
0.6+0.7bar+0.4 7bar​

Answer 1

Answer:

0.6=6/10

Converting 0.7bar into rational no. :

Let x=0.7bar......(1)

Then multiplying x with 10 as one digit is repeating after the decimal

So, 10x=7.7bar.....(2)

Now subtracting (1) from (2)

Then, 10x-x=7.7bar-0.7bar

9x=7

x=7/9

and the same way converting 0.47bar as rational no. :

Let y=0.47 bar.........(1)

Multiplying y with 100 as two digits are repeating after the decimal.

100y=47.47bar.........(2)

Subtracting (1) from (2):

100y-y=47.47bar-0.47bar=47

99y=47

y=47/99

Hence, 0.6+0.7bar+0.47bar=6/10+7/9+47/99

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