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Balanced ternary
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==Irrational numbers== As in any other integer base, algebraic irrationals and transcendental numbers do not terminate or repeat. For example: :{| class="wikitable" !Decimal !! Balanced ternary |- |<math>\sqrt{2}=1.4142135623731\ldots</math> || <math>\sqrt{\mathrm{1T}}=\mathrm{1.11T1TT00T00T01T0T00T00T01TT\ldots}</math> |- |<math>\sqrt{3}=1.7320508075689\ldots</math> || <math>\sqrt{\mathrm{10}}=\mathrm{1T.T1TT10T0000TT1100T0TTT011T0\ldots}</math> |- |<math>\sqrt{5}=2.2360679774998\ldots</math> || <math>\sqrt{\mathrm{1TT}}=\mathrm{1T.1T0101010TTT1TT11010TTT01T1\ldots}</math> |- |<math display="inline">\varphi=\frac{1 + \sqrt{5}}{2}=1.6180339887499\ldots</math> || <math display="inline">\varphi=\frac{1 + \sqrt{\mathrm{1TT}}}{\mathrm{1T}}=\mathrm{1T.T0TT01TT0T10TT11T0011T10011\ldots}</math> |- |<math>\tau=6.28318530717959\ldots</math> || <math>\tau=\mathrm{1T0.10TT0T1100T110TT0T1TT000001}\ldots</math> |- |<math>\pi=3.14159265358979\ldots</math> || <math>\pi=\mathrm{10.011T111T000T011T1101T111111}\ldots</math> |- |<math>e=2.71828182845905\ldots</math> || <math>e=\mathrm{10.T0111TT0T0T111T0111T000T11T}\ldots</math> |} The balanced ternary expansions of <math>\pi</math> is given in [[OEIS]] as {{OEIS link|A331313}}, that of <math>e</math> in {{OEIS link|A331990}}.
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