1) 3/8
0.375
8)3.0'0'0'0 The first integer 3 cannot be divided by 8, this means
-24 the decimal number will start with zero, put the zero
60 above the line and the decimal dot. This allows you
-56 to use the first integer 3 and add a zero to form 30.
40 30 is not a multiple of 8, so look for the closest value, in
-40 this case, is 8*3=24. Next subtract 24 from 30 and write
0/ the remainder below it.
Six alone cannot be divided by 8 so borrow a zero from
above and divide 60 by 8. The closer value is 8*7=56.
Write 7 above the answer line and subtract 56 from 60.
4 cannot be divided by 8, so borrow a 0 from above
and turn it into 40. Forty is multiple of 8, if you multiply
8*5=40, so following the method, multiply 8 by 5 and
subtract 40.
After 4 operations you've reached the solution with remainder zero, i.e. there is nothing more to divide.
This means that 3/8=0.375, the fact that you reched zero means that this is a terminating operation.
2) 7/18
Display the denominator first, then a parenthesis, then the numerator. Above the numerator there will be the answer line:
0.388
18)70'0'0'00 7 is not divisible by 18, at least not directly, since you
-54 cannot divide it, same as in the last division, you have to
160 put the result zero for the first operation and follow it by
-144 the decimal point. This decimal point allows you to add
160 succesive zeros in order to continue the division.
-144 Second step, check if 70 is multiple of 18.
16/ 18*2=36; 18*3=54; 18*4=72, the closer multiple is
18*3=54, so write 3 in the answer line and subtract 54
from 70.
The remainder 16 is not divisible by 18, so add a zero
and turn it into 160. Now look for a multiple of 18 that
produces a result equal or close to 160.
The closer multiple is 18*8= 144 becuase the next one
18*9=162 is too big.
The remainder is 16 again so repeat the operation.
As you can see after the third time the remainder continues to be 16, this means that no matter how many times you divide 160 by 18, the result won't change. The decimal value will repeat itself to infinity.
So after 3 operations we determined that 7/18=0.3888888
There is no need to do more than this because the result won't change, you'll never reach remainder=0
The decimal value equivalent to 7/18 is repeating.