Question

Write the decimal expansion of $\frac{1}{14}$ up to 7 decimal places.

Answer 1

14)1.0000000(0.0714285
0
10
0
100
98
20
14
60
56
40
28
120
112
80
70
10
Here we see that after carrying division 8 times we return with a remainder 10 which is the dividend at the second step of division continues after 6 steps. Thus the string 714825 respects in the quotient infinitely often. Thus the decimal expansion of $\frac{1}{14}$ looks like 0.0714825714824 ...(Here remainder is never 0).