Revision #912 → #1535 · back to history
addedRepeating decimal61b1f4fcd873
addedRational iff repeating or terminating969938c6e15c
added1/3 = 0.333...0959964dd838
added3227/555 = 5.8144144...e5d88d305d2b
added593/53 repeats 13-digit patternc78d1fe0559c
addedRepetend / reptend3f2af31cad8a
addedTerminating decimal as decimal fractiona8e1ca7b1f76
addedAlternative repeating-9 representation9d151c0274d7
addedIrrational numberd676bde8feb0
added5/74 long division95243b56b289
addedRemainder at step k formulaa1ac75684192
addedFinitely many remainders forces termination or repetition13113507bf41
addedDivision eventually repeats remainder1d77ed050766
addedBase-10 repeating iff denominator has prime factor other than 2 or 5ce67c335660a
addedRepeating decimal satisfies linear equation0543e293c2ba
addedSolve for 5.8144144...f77a63c4ca5f
addedFormal proof of rationalityc4ee919fdeea
addedRepetend length equals order of 10 mod pf6f2320934d3
addedDigital root of repetend is 919ddb25bf894
addedCyclic numberf366cf02a22f
addedCyclic fractions 1/7, 1/17, ...c2c80d46627c
addedProper multiples are rotations1e412ff7f0d9
addedCyclic remainders in long division of 1/73340ddca0f8f
addedCyclic repetend splits into nines' complement halves0bdd23c2fa89
addedRotated repetends increase8c71b597f175
addedProper prime474ec2aada35
addedProper prime characterization7e395a4af646
addedFull reptend safe prime gives pseudo-random digits1046404c09eb
addedNon-cyclic reciprocals of primes97d729acd7ea
addedPeriod from 10^(p-1) - 1 divisibility776a0e4a7e79
addedMultiples of 1/13 form two repetend setscdcf02c379e9
addedProper multiples of 1/p form n subsetsf2ce07176c8e
addedTotient rule for repetend length5e1f0927b034
addedFull repetend primed0a7a1663b98
added1/49 repeating decimal6ab2d64a32c5
addedCarmichael's theorem on period of 1/p^216d6ace36518
addedPeriod of 1/p^2 is usually pT_p0d902236734a
addedPeriod of 1/p^k usually p^(k-1) T_p87d97f69bf66
added1/119 period9f973edd82e8
addedPeriod of 1/pq is LCM of periods828a3ea84704
addedGeneral period formula for product of prime powers166d71416fb3
addedReciprocals not coprime to 10 are eventually periodice52a2f5fa1f3
addedTransient and repetend structure9e035acd9999
added1/28 = 0.03 5714285c56cb1cf753
addedConverting repeating decimal to fraction661765430361
addedShortcut: repetend of n nines fractiondc962e5a840c
addedGeneral formula for n-digit period after decimal point518b59034ee2
addedFraction with n-digit repeating block immediately after decimal2f1e3aa9df2c
added0.444... = 4/9 etc.80154613c2a3
addedAdd k zeros to denominator for k leading zeros35d0dd0e43b6
added0.000444... = 4/90007ebb0c98363c
addedDecompose any repeating decimal as sum83880deb5c98
added1.23444... = 1111/9002bbd03c4ecef
addedDenominator is (10^n - 1) 10^k8bc81ab16ea8
addedPeriod is smallest n with d | 10^n - 186f5fb8e5847
addedPeriod of 2/7 is 643ba04d3fcd6
addedCompressed form of generating fractionbc77b609e8dd
addedRepeating decimal as geometric series82cd26a5c00b
addedCyclically permuted integer 102564 × 4c1e3e626bd56
addedPeriod of 1/k is at most k - 1fb0417987e77
addedPeriod of 1/p divides p - 1eff946098fdf
addedPeriod of composite 1/k strictly less than k - 1b44453367065
addedPeriod of c/k equals period of 1/k0835ffe387e8
addedTransient length and period for k = 2^a 5^b n03151bd59f72
addedPeriod of product of distinct primesfcd05cabbc83
addedPeriod of 1/(k k') is LCM3f0eb159273a
addedEach digit appears h times in proper prime repetend93a6b93fe3d3
addedTerminating sequence iff prime factors of denominator are factors of base2e7dbe6d9350
addedOrder homomorphism from strings to realsa1db423defa4
addedRepetend length in arbitrary base87c0bc5d8ac4
addedIrrational in arbitrary base58bb089e59e4
addedDuodecimal expansionsa535f1f19df5
addedBase shift identity598b3f83f1d8
addedAlgorithm for positive basese35247b7ce57