Express 0.64+0.8bar+ 0.5bar in the form of p/q

1.	Express 0.64+0.8bar+ 0.5bar in the form of p/q
Answer» Hey there!! All we have to do here is convert all the number in a rational form. That is p/q form and upon adding these numbers, we get our desirable answer. First, let's convert 0.8bar 0.8 bar = 0.888888888888888..... ----- ( x ) The PERIODICITY is 1, so let's MULTIPLY it with 10 0.8 bar × 10 = 8.888888888 ----- ( 10x ) Now, all we have to do it subtract x from 10x. 10x = 8.88888 x = 0.888888 ____________ 9x = 8 x = 8/9; 0.8 bar is 8/9 ______________________________________________ Now, let's convert 0.5 bar 0.5 bar = 0.55555555 ---- ( x ) Periodicity is 1 again, hence we multiply it with 10 0.5 bar × 10 = 5.555555 ---- ( 10x ) _________ 10x = 5.555 x = 0.555 _____________ 9x = 5 x= 5/9; 0.5 bar is 5/9 ___________________________________________ Now, convert 0.64 = 64/100 = 32/50 = 16/25 Now, let's add all the numbers. ( 16/25 ) + ( 8/9 ) + ( 5/9 ) Doing it, we get 469/225 Hence, the answer is 469/225 Hope it HELPS! :)

Answer»

Hey there!!

All we have to do here is convert all the number in a rational form. That is p/q form and upon adding these numbers, we get our desirable answer.

First, let's convert 0.8bar

0.8 bar = 0.888888888888888..... ----- ( x )

The PERIODICITY is 1, so let's MULTIPLY it with 10

0.8 bar × 10 = 8.888888888 ----- ( 10x )

Now, all we have to do it subtract x from 10x.

10x = 8.88888

x = 0.888888

____________

9x = 8

x = 8/9; 0.8 bar is 8/9

______________________________________________

Now, let's convert 0.5 bar

0.5 bar = 0.55555555 ---- ( x )

Periodicity is 1 again, hence we multiply it with 10

0.5 bar × 10 = 5.555555 ---- ( 10x )

_________

10x = 5.555

x = 0.555

_____________

9x = 5

x= 5/9; 0.5 bar is 5/9

___________________________________________

Now, convert 0.64 = 64/100 = 32/50 = 16/25

Now, let's add all the numbers.

( 16/25 ) + ( 8/9 ) + ( 5/9 )

Doing it, we get 469/225

Hence, the answer is 469/225

Hope it HELPS! :)

Discussion