Question

express in p/q form 0.888.......

Answer 1

let

1) x=0.8888...
2) 10x=8.8888...

Subtract 1 from 2

10x-x=8.8888-0.8888
9x=8
x=8/9

ans. is 8/9

Answer 2

Answer:

0.888 = 111/125

Step-by-step explanation:

p/q form is the form of fractions.

We have 0.888, which is a number with 3 decimal points. We however want to convert it to a fraction. We have known that this number has 3 decimal points because we have counted the number of digits we have from the decimal ponts and have found that we have 3 digits.

This number 0.888 is also 0.888/ 1, which is just but the same thing. Now that we have found out that we have 3 decimal points, we will multiply both the numerator which is 0.888 and the denominator by 1000 so we can find a whole number and get rid of the decimal points we have.

(0.888 × 1000) / ( 1 × 1000)

We then have

888/1000

So we have now gotten rid of the decimal points and we now have a fraction. You have to note that a fraction cannot have any decimals whether in the numerator or the denominator.

In our fraction, 888/1000 ,we have to look for a common divisor, that divides through the numerator and the denominator, so we can leave the fraction in the simplest way possible.

We start with dividing both the numerator and the denominator by 2, which gives us

444/500

We further dividing the numerator and the denominator by 2 to get

222/250

Further dividing the numerator and the denominator by 2 we get

111/125

So when we get here, 2 cannot divide through them any further, we move to 3, it can divide the 111 without a remainder, but not 125, so we move to other prime numbers, 5,7,9,11, none of them can divide through the numerator and the denominator without a remainder.

Therefore our final answer becomes

111/125