# Numerical Calculations

Maple performs mathematical calculations swiftly and accurately. Unlike a calculator, Maple's worksheet can keep a permanent record of your calculations for later use.

```> 123.4*8.2^3;

68038.8112

> (23.4*43)/(43.5-(3.2*2))+(12.4*34.8);

458.6412938```

Maple also recognizes many special operators such as factorial, square roots, least common divisor, etc. For example:

```> 13!;

6227020800

> (5^8)/(3*Pi^2)*sqrt(5);

1/2
5
390625/3 ----
2
Pi
```

Note that Maple kept answer in the form of an expression, i.e., it does not round off the answer. Maple will allow this expression to carry over as is so that rounding errors do not plague the user. If one wants to see the final answer as a decimal floating point, the `evalf` command can be used. Also note that the quotation mark (") is used to represent the last expression computed:

```> evalf(");

29500.13725
```
Maple also calculates finite and infinite sums and products:

```> Sum((2*i+5)/(3*i^2-5),i=1..10);

10
-----
\     2 i + 5
)   --------
/       2
----- 3 i  - 5
i = 1

> value(");

29392799449
- -----------
48571966058

> evalf(");

-.6051391746

> Product((3*Pi*i-5)/(2*i^2-Pi),i=1..10);

10
--------'
'  |  |    3 Pi i - 5
|  |    ----------
|  |        2
|  |     2 i  - Pi
i = 1

> value(");

(3 Pi - 5) (6 Pi - 5) (9 Pi - 5) (12 Pi - 5) (15 Pi - 5) (18 Pi - 5)

/
(21 Pi - 5) (24 Pi - 5) (27 Pi - 5) (30 Pi - 5)  /  ((2 - Pi) (8 - Pi)
/

(18 - Pi) (32 - Pi) (50 - Pi) (72 - Pi) (98 - Pi) (128 - Pi) (162 - Pi) (200 - Pi))

> evalf(");

-1.089588169
```

Notice the above gets a little messy on an ASCII screen. It looks better on an X-Window session

One can round off the value to any number of decimal places desired:

```> 5/3;

5/3

> evalf(",3);

1.67
```

Maple also utilizes complex numbers:

```> (12+8*I)*(9+3*I)/(2+I);

276/5 + 132/5I
```