# Small Calculations

It is common for students to have mastered the conceptual features of a problem or estimation and then make an error on the calculator. This is very frustrating to the student and since there is no record of the computation on most calculators, very difficult to find the error.

This section discusses how we enter mathematical expressions into calculators and computers and calculator tools that make it easier to inspect our work.

### Basic computations

* Addition (+)
* Subtraction (-)
* Multiplication (\*)
* Division (/)
* Exponentiation (^ or \*\*)

To perform basic calculations with numbers, we can type numbers into the computer and use the symbols above to perform the calculation.

### Order of Operations

How does the computer interpret a long calculation

$$1 + 2 \* 3 - 4 / 5 = ?$$

### PEMDAS

You may be familiar with the PEMDAS order of operations

* Parenthesis
* Exponents
* Multiplication and Division
* Addition and Subtraction

### Commutative operations

$$1 \* 2 \* 3 = 3 \* 2 \* 1$$

$$1 \* 2 / 3 = 1 / 3 \* 2$$

### Commutative operations

$$1 + 2 + 3 = 3 + 2 + 1$$

$$1 + 2 - 3 = 1 - 3 + 2$$

### Scientific Notation

$$6 \cdot 10^3$$ is entered as `6E3`.

This key is often on a calculator as "E" or "EE". It is much easier and less error-prone to use this instead of "6 \* 10 x^y 3".

### Know your calculator

$$1 + 2 \* 3 = ?$$

The answer can vary with your calculator...

## Calculators

There are calculator apps online that are much better for calculations than the iOS and Android default applications.

[Geogebra Sci Calc](https://www.geogebra.org/calculator?lang=en)
