Using brackets in computing is sometimes an unnecessary complication. Using post-fix expressions ensures that only one order of operation is needed. Postfix is another name for 'reverse Polish' notation.

```
Infix: 38 + y
Postfix: 38 y +
```

### Converting Infix to RPN

```
((42*3) / 150) + 9
Step 1: Add brackets where needed:
(((42*3) / 150) + 9)
Step 2: Start from the inside bracket, and move operators to the right-hand side of the brackets they're in.
(((42 3 * ) 150 /) 9 +)
Step 3: Remove all brackets.
42 3 * 150 / 9 +
```

### Converting RPN to Infix

```
42 3 * 150 / 9 +
Step 1: Add brackets.
(((42 3 *) 150 /) 9 +)
Step 2: Move operators to their infix positions.
(((42 * 3) / 150) + 9)
Step 3: Remove unnecessary brackets.
42 * 3 / 150 + 9
```