Question

express each of the following decimal number in the p/q form 1.) 0.5 bar 2.) 3.8 bar 3.) 0.36 bar

Answer 1

Answer:

0.555.... = 5/9

3.888... = 35/9

36.363636... = 4/11

Step-by-step explanation:

1)

We are given that

0.5 bar = 0.555...

Let

x = 0.555...

Multiplying by 10 on both sides we get

10x = 5.555...

Subtracting first equation from second equation

10x - x = 5.555... - 0.555... = 5

      9x = 5

        x = 5/9

So

0.555.... = 5/9

2)

We are given that

3.8 bar = 3.888...

Let

x = 3.888...

Multiplying by 10 on both sides we get

10x = 38.88...

Subtracting first equation from second equation

10x - x = 38.88... - 3.888... = 35

      9x = 35

        x = 35/9

So

3.888... = 35/9

3)

We are given that

0.36 bar = 0.363636...

Let

x = 0.363636...

Multiplying by 100 on both sides we get

100x = 36.363636...

Subtracting first equation from second equation

100x - x = 36.363636... - 0.363636... = 36

     99x = 36

         x = 36/99 = 12/33 = 4 / 11

So

36.363636... = 4/11

Answer 2

Answer:

Ok Thank you for answering