Observations on Reciprocals of Leftins
Table of Reciprocals
- All rationals have reciprocals in all bases.
- Rationals have one uniquely determined reciprocal to the same number of significant digits as the original number.
- If an integer shares factors with the number base, its reciprocal will require digits to the right of the decimal point.
- The number of digits needed to the right of the decimal point for the reciprocal of an integer...
- If the number base is prime, it's equal to the number of 0's the number ends with.
- If the number base is a prime raised to a power greater than 1, it's equal to the number of 0's the number ends with plus an extra digit if the last non-0 digit is a power of the prime.
- If the number base is the product of at least two different prime numbers, it's unrelated to the final digits.
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© Scott Sherman 1999