Question

Express 0.123_ as a rational number in the form p /q where p and q are integers and q is not equal to 0 ( bar is on 123)​

Answer 1

Answer:

Let x = 0.123 (bar)

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Multiply by 100,

100*x = 100*0.123 (bar)

100x = 12. 3(bar)

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As there is one number (3) under bar, multiply by 10

10 *100x = 10 * 12.3 (bar)

1000x = 123. 3 bar

subtract 100x from both sides,

1000x = 123.3 (bar)

-100x = -12. 3 (bar)

900x = 111 [bar will cancel]

x= \frac{111}{900}x=

900

111

Now,

0.123 (bar on 3) in p/q form is \frac{111}{900}

900

111

i hope this will help you

Answer 2

let x=0.123~---(1)

multiply both sides with 1000

1000x=123.123~-----(2)

subtract eq-1 from eq-2

=999x=123

x=123/999

therefore p/q form of 0.123~= 123/999