7.3.1 Evaluating a real at a given precision
A real number is an exact number and its numeric evaluation at a given
precision is a floating number represented in base 2. The precision of
a floating number is the number of bits of its mantissa, which is at
least 53 (hardware float numbers, also known as double).
Floating numbers are displayed in base 10 with a number of digits
controlled by the user either by assigning the
Digits
variable or by modifying the CAS configuration (see
Section 2.5.7, item 2.5.7). By default,
Digits is equal to 12.
The number of digits displayed controls the number of bits of the
mantissa; if Digits is less than 15, 53 bits are used, if
Digits is strictly greater than 15, the number of bits is a
roundoff of Digits times log2(10).
An expression can be coerced into a floating number with the
evalf command
(see Section 7.3.1). The evalf
command may have an optional second argument which will specify the
precision to use.
Note that if an expression contains a floating number, evaluation will
try to convert other arguments to floating point numbers in order to
coerce the whole expression to a single floating number.
Examples
Input for a result with 30 digits:
Input for the numeric value of eπ√163:
|
0.262537412640768743999999999985×108
| | | | | | | | | | |
|
Note that Digits is now set to 30. You could have entered:
evalf(exp(pi*sqrt(163)),30) |
if you didn’t want to change
the value of Digits.