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Sayılar Teorisi
=> Algebraic Curves-Mordell Curve
=> Algebraic Curves-Ochoa Curve
=> Algebraic Integer
=> Algebraic Number
=> Algebraic Number Theory
=> Chebotarev Density Theorem
=> Class Field
=> Cyclotomic Field
=> Dedekind Ring
=> Fractional Ideal
=> Global Field
=> Local Field
=> Number Field Signature
=> Picard Group
=> Pisot Number
=> Weyl Sum
=> Casting Out Nines
=> A-Sequence
=> Anomalous Cancellation
=> Archimedes' Axiom
=> B2-Sequence
=> Calcus
=> Calkin-Wilf Tree
=> Egyptian Fraction
=> Egyptian Number
=> Erdős-Straus Conjecture
=> Erdős-Turán Conjecture
=> Eye of Horus Fraction
=> Farey Sequence
=> Ford Circle
=> Irreducible Fraction
=> Mediant
=> Minkowski's Question Mark Function
=> Pandigital Fraction
=> Reverse Polish Notation
=> Division by Zero
=> Infinite Product
=> Karatsuba Multiplication
=> Lattice Method
=> Pippenger Product
=> Reciprocal
=> Russian Multiplication
=> Solidus
=> Steffi Problem
=> Synthetic Division
=> Binary
=> Euler's Totient Rule
=> Goodstein Sequence
=> Hereditary Representation
=> Least Significant Bit
=> Midy's Theorem
=> Moser-de Bruijn Sequence
=> Negabinary
=> Negadecimal
=> Nialpdrome
=> Nonregular Number
=> Normal Number
=> One-Seventh Ellipse
=> Quaternary
=> Radix
=> Regular Number
=> Repeating Decimal
=> Saunders Graphic
=> Ternary
=> Unique Prime
=> Vigesimal
Ziyaretçi defteri
 

Regular Number

A regular number, also called a finite decimal (Havil 2003, p. 25), is a positive number that has a finite decimal expansion. A number such as 1/3=0.33333... which is not regular is said to be nonregular.

If r=p/q is a regular number, then

r = (a_1)/(10)+(a_2)/(10^2)+...+(a_n)/(10^n)
(1)
= (a_110^(n-1)+a_210^(n-2)+...+a_n)/(10^n)
(2)
= (a_110^(n-1)+a_210^(n-2)+...+a_n)/(2^n·5^n).
(3)

Factoring possible common multiples gives

 r=p/(2^alpha5^beta),
(4)

where p≢0 (mod 2, 5).

The denominators of the first few regular unit fractions are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, ... (Sloane's A003592), which have decimal expansions 1, 1/2=0.5, 1/4=0.25, 1/5=0.2, 1/8=0.125, 1/10=0.1, 1/16=0.0625, 1/20=0.05, 1/25=0.04, 1/32=0.03125, 1/40=0.025, 1/50=0.02, ....

The number of decimal digits in a regular number is given by max(alpha,beta) (Wells 1986, p. 60). The numbers of digits in the regular unit fractions are 1, 2, 1, 3, 1, 4, 2, 2, 5, 3, 2, 6, 4, 2, 3, ... (Sloane's A117920).

 

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