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RealDigits

RealDigits[x]
gives a list of the digits in the approximate real number x, together with the number of digits that are to the left of the decimal point.
RealDigits[x, b]
gives a list of base-b digits in x.
RealDigits[x, b, len]
gives a list of len digits.
RealDigits[x, b, len, n]
gives len digits starting with the coefficient of bn.
  • RealDigits gives the most significant digits first, as in standard positional notation.
  • RealDigits[x] normally returns a list of digits of length Round[Precision[x]].
  • RealDigits[x] and RealDigits[x, b] normally require that x be an approximate real number, returned for example by N. RealDigits[x, b, len] also works on exact numbers.
  • For integers and rational numbers with terminating digit expansions, RealDigits[x] returns an ordinary list of digits. For rational numbers with non-terminating digit expansions it yields a list of the form {a1, a2, ..., {b1, b2, ...}} representing the digit sequence consisting of the ai followed by infinite cyclic repetitions of the bi.  »
  • RealDigits[x, b, len, n] starts with the digit which is the coefficient of bn, truncating or padding with zeros as necessary.  »
  • RealDigits[x, b, len, -1] starts with the digit immediately to the right of the base-b decimal point in x.
  • The base b in RealDigits[x, b] need not be an integer. For any real b such that b>1, RealDigits[x, b] successively finds the largest integer multiples of powers of b that can be removed while leaving a non-negative remainder.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Give the list of digits and exponent:
Give 25 digits of Pi in base 10:
Give 25 digits of 19/7:
Give an explicit recurring decimal form:
Give the list of digits and exponent:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Give 25 digits of Pi in base 10:
In[1]:=
Click for copyable input
Out[1]=
 
Give 25 digits of 19/7:
In[1]:=
Click for copyable input
Out[1]=
Give an explicit recurring decimal form:
In[2]:=
Click for copyable input
Out[2]=
Scope   (3)
Base-2 digits:
20 digits starting with the coefficient of 10^(-5):
20 digits starting with the coefficient of 10^5:
Non-integer bases are allowed:
Generalizations & Extensions   (2)
RealDigits gives Indeterminate if more digits than the precision are requested:
Start at the coefficient of 10^(-15):
Include only digits that are determined by the precision available:
Applications   (6)
The 10000^(th) digit of Pi is an 8:
Number of 1s in the first million base-2 digits of Pi:
Distribution of first 100000 digits of Pi in base 47:
Fibonacci representations of integers:
Binary representation of a machine number:
MachinePrecision is equal to the number of bits times log_(10)(2):
Get the next larger machine number:
The spacing between these numbers is 2(e-1) $MachineEpsilon:
Find the error in representing 1/10 with a machine number:
The next smaller machine number is farther away:
Properties & Relations   (1)
The default number of digits returned is determined by the precision of the number:
Possible Issues   (2)
Digits unknown at the available precision are filled in as Indeterminate:
For non-binary bases, the digits given may not be enough to reconstruct the number exactly:
More than Round[MachinePrecision] decimal digits are required to separate x from 1:
InputForm uses a sufficient number of digits to uniquely reconstruct the number:
Neat Examples   (1)
A hundred digits of Pi starting with the millionth digit:
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