### 2.9.1 Eval a real at a given precision : `evalf` and `Digits`, `DIGITS`)

- 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 it’s 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. 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 the log of 10 in base 2.
- An expression is coerced into a floating number with the `evalf` command. `evalf` may have an optional second argument which will be used to evaluate with a given precision.
- 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.

Input :

`1+1/2`

Output :

`3/2`

Input :

`1.0+1/2`

Output :

`1.5`

Input:

`exp(pi*sqrt(20))`

Output :

`exp(pi*2*sqrt(5))`

With `evalf`, input :

`evalf(exp(pi*2*sqrt(5)))`

Output :

`1263794.75367`

Input :

`1.1```^```20`

Output :

`6.72749994933`

Input :

`sqrt(2)```^```21`

Output :

`sqrt(2)*2```^```10`

Input for a result with 30 digits :

`Digits:=30`

Input for the numeric value of eπ√163:

`evalf(exp(pi*sqrt(163)))`

Output :

`0.262537412640768743999999999985e18`

Note that `Digits` is now set to 30. If you don’t want to change the value of `Digits` you may input

`evalf(exp(pi*sqrt(163)),30)`