- The solution consists of a digit part which is zero always.
- The decimal part repeats after every (n – 1) digits.
- The decimal part is calculated by multiplying (or dividing) each successive digit with a calculated fixed number.
- The carry is added to (or subtracted from) the next successive digit.
- Prime numbers ending with 1.
E.g.:
Consider a number ab.
Then the fixed multiplicand is = ab - a
· 1/11 = 11 - 1 = 10. · 1/31 = 31 - 3 = 28.
· 1/71 = 71 - 7 = 64.
· 1/101 = 101 - 10 = 91.
· 1/131 = 131 - 13 = 118.
· 1/971 = 971 - 97 = 874.
- Prime numbers ending with 7.
E.g.:
Consider a number ab.
Then the fixed multiplicand is = (a × b) + 5.
· 1/7 = (0 × 7) + 5. · 1/17 = (1 × 7) + 5.
· 1/977 = (97 × 7) + 5.
- Prime numbers ending with 9.
E.g.:
Consider a number ab.
Then the fixed multiplicand is = Ten’s digit + 1
· 1/19 = 1 + 1 = 2. · 1/29 = 2 + 1 = 3.
· 1/1129 = 112 + 1 = 113.
- Prime numbers ending with 3.
E.g.:
Consider a number ab.
Then the fixed multiplicand is = (a × b) + 1.
· 1/13 = (1 × 3) + 1. · 1/23 = (2 × 3) + 1.
· 1/1123 = (122 × 3) + 1.
Some solutions:
1/7 = 0.142857…
1/13 = 0.076923076923…
1/17 = 0.0588235294117647…
1/19 = 0.052631578947368421…
1/23 = 0.0434782608695652173913…
1/29 = 0.0344827586206896551724137931…