Answer:
[tex]\frac{7}{9}=0.77777...[/tex]
Step-by-step explanation:
The division is
[tex]\frac{7}{9}[/tex]
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
[tex]\frac{70}{9}=0.[/tex]
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
[tex]\frac{70}{9}=0.7[/tex]
Now, this process repeats infinitely, because the reminder is always 7.
Therefore, the result of the division is
[tex]\frac{7}{9}=0.77777...[/tex]
