Question

express 0.45bar in the form of p/q

Answer 1

Hope it helps.............

Answer 2

Given:

$0.\bar{45}$

To Find:

Express it in the form of p/q

Solution:

To express in the form of p/q we will let this value be equal to x. Please note that it can be expressed in p/q form only if the decimal is repeating non terminating decimals. now let x=0454545..

$x=0.454545...$    -(1)

Now multiply both sides by 100( we choose it to multiply by 10 100 1000 etc depending on the digits after which they are repeating if they are repeating after 4 digits then multiply by 10000)

$100x=45.454545...$      -(2)

Now we subtract equation 2 with 1 getting

$99x=45\\x=\frac{45}{99}$

Now simplifying it to get the lowest value

$x=\frac{45}{99} \\=\frac{5}{11}$

Now if we divide 5 by 11 we will get the decimals as 0.454545...

Hence, 0.45bar in the form of p/q will be 5/11.