Numbers and Precision

Variable-precision arithmetic and elementary number-theoretic operations

The Symbolic Math Toolbox™ can perform numeric calculations with variable precision by using vpa. For details, see Increase Precision of Numeric Calculations. To understand when to use symbolic, variable-precision, or double-precision arithmetic, see Choose Numeric or Symbolic Arithmetic. The Symbolic Math Toolbox also provides functions for rounding operations and for working with complex numbers.

Functions

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Precision Control

`digits`	Change variable precision used
`double`	Convert symbolic values to MATLAB double precision
`vpa`	Variable-precision arithmetic (arbitrary-precision arithmetic)
`vpaintegral`	Numerical integration using variable precision
`vpasolve`	Solve symbolic equations numerically
`vpasum`	Numerical summation using variable precision (Since R2020b)

Operations on Numbers

`imag`	Imaginary part of complex number
`real`	Real part of complex number
`dec2bin`	Convert symbolic integer in decimal to binary representation
`dec2hex`	Convert symbolic integer in decimal to hexadecimal representation

Topics

Choose Numeric or Symbolic Arithmetic
Compare and contrast double-precision, variable-precision, and symbolic arithmetic.
Numeric to Symbolic Conversion
Convert floating-point numbers to exact symbolic numbers.
Increase Precision of Numeric Calculations
Increase precision arbitrarily with variable-precision arithmetic.
Recognize and Avoid Round-Off Errors
Round-off errors in symbolic and variable-precision calculations.
Increase Speed by Reducing Precision
Increase speed of calculations by reducing precision of calculations.

Featured Examples

Prime Factorizations

Use some elementary functions on sym objects using the Symbolic Math Toolbox™.

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Handling Large Integers to Solve the 196 Problem

Work with large integers and their decimal representation using the Symbolic Math Toolbox™.

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Compute Binomial Coefficients Exactly

Get precise values for binomial coefficients and find probabilities in coin-tossing experiments using the Symbolic Math Toolbox™.

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Find Almost Integers with High-Precision Arithmetic

Find almost integers, or numbers that are very close to integers, using variable-precision arithmetic in Symbolic Math Toolbox.

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Decimal Digits of PI

Use variable-precision arithmetic to investigate the decimal digits of pi using Symbolic Math Toolbox™.

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