Symbolic Floating-Point Evaluation

To evaluate an expression using symbolic floating-point evaluation, select the expression and either:

Then type a positive integer, specifying the number of digits in the floating-point evaluation, in the placeholder that appears, and press [Enter].

Note: The integer argument after "float" is not required. By default, "float" evaluates the result to 20 digits.

Examples:

The following evaluates π to 25 decimal places:

π float, 25→ 3.141592653589793238462643

You can also force symbolic floating point evaluation with just the symbolic equal sign by using decimal numbers rather than integers.

example of floating point evaluation

Caution: You should avoid defining a variable to be the output of float with a small integer argument, as the result will not be very accurate. For example, if you set

x:= π float, 4 → 3.142

x is a poor approximation of π. Compare this with setting a variable equal to π without using float.

y:= π

When Number of decimal places is set to its maximum value of 17, you can see the difference in accuracy between x and y.

x = 3.142

y = 3.141592653589793

Note that Number of decimal places only affects how results are displayed, not their actual values. If you change Number of decimal places to 3, only 3 decimal places for y are displayed, but the value of y remains the same.

If you need to evaluate a symbolic expression numerically, you can usually do so using the numerical equal sign. However, some symbolic functions cannot be evaluated with the numerical equal sign. To evaluate these, use the symbolic equal sign with the keyword "float," which performs symbolic floating-point evaluation.

For example, you can evaluate the symbolic function Zeta, which calculates the Riemann Zeta function, to 7 digits as follows:

Evaluating Zeta(1/2) with float

Notes: