Question

Use long division to determine the decimal equivalent of 7 over 9.

Answer 1

0.7 repeated (little line over the 7)

Answer 2

`(7)/(9)=0.77777...`

Explanation:

The division is

`(7)/(9)`

So, as you can see, the divisor is greater than the dividend, when this happens, we need to add a decimal point to the quotient, so at the moment, the result is

`(70)/(9)=0.`

With this decimal point, we are allowed to add a zero to the dividend, now we can look for a number which product with 9 results near 70, that numbers is 7, because 9x7 = 63. Then, we subtract, 70-63 = 7, and there is added automatically the zero from the decimal points, so at the moment the result is

`(70)/(9)=0.7`

Now, this process repeats infinitely, because the reminder is always 7.

Therefore, the result of the division is

`(7)/(9)=0.77777...`