# 1.3 Itse1359-1020-numbers  (Page 6/6)

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## Forcing multiplication to be performed first

In the second expression, the code in Figure 12 forced Python to perform the multiplication first (which it does anyway by default, but the parentheses make that more obvious) . This produced an intermediate value of 20. The remaining part of the overallexpression was then evaluated by adding the intermediate value to 3 producing an output of 23.

Hopefully, you get the picture. By using parentheses to group the terms in an expression, you have total control over the order in which the arithmeticoperations are performed, without having to memorize a precedence table.

## Nested parentheses

Parentheses can be, and often are nested to provide greater control over the order of the operations as shown in Figure 13 .

Figure 13 . Nested parentheses.
```>>>(3+(5*4))*14 # nested parentheses 322>>>```

In this case, Python evaluates the expressions inside the innermost parentheses first, and then works from the inside out evaluating each pair ofparentheses along the way.

## Negative integer division

When I learned to do long division in the second grade, I didn't know about positive and negative numbers yet, so I didn't learn about remainders when oneof the operands is negative and the other is positive. I suspect that you didn't either.

Figure 14 shows how negative integer division and modulus works in Python.

Figure 14 . Negative integer division.
```>>>7 // -3 -3>>>7 % -3 -2>>>7 // 3 2>>>7 % 3 1>>>```

You may find these results surprising. I'm not going to try to explain it. I just want to make you aware that the behavior of integer division and integer modulus is different when the operandshave different signs. I will leave it as "an exercise for the student" to think about this and come to a mental reconciliation with the facts as presented here.

## Complex numbers

Python also provides a significant level of support for doing arithmetic with complex numbers. Since this is a very specialized area, which is probably ofinterest to only a small percentage of potential Python users, I'm not going to provide any of the details. If this is something that interests you, see Standard Library -- Mathematical functions for complex numbers for more information.

## Programming errors

Sometimes, you may make an error and enter an expression that can't be evaluated. In this case, you will get an error message. A typical error messagethat was produced by the command-line interface is shown in Figure 15 .

Figure 15 . An error on the command-line interface.
```>>>3 + 5a File "<stdin>", line 1 3 + 5a^ SyntaxError: invalid syntax>>>```

Note that the IDLE GUI interface doesn't provide as much information as the command-line interface for the same error. Only the SyntaxError message appears on the IDLE GUI interface as shown in Figure 16 .

Figure 16 . An error on the IDLE GUI interface.
```>>>3 + 5a SyntaxError: invalid syntax>>>```

Not shown here, however, is the fact that the 5a is highlighted with a red background in the GUI interface. Also, the error message is displayed inred.

Referring back to Figure 15 , this error message means that the Python interpreter doesn't know how to add the value 3 to the value 5a. I will discuss error messages in moredetail in a future module. I just wanted to show you a programming error here at the beginning. (Note the ^ character in Figure 15 pointing upward to the "a"character. This is a pointer to the source of the error.)

## Miscellaneous

This section contains a variety of miscellaneous information.

Housekeeping material
• Module name: Itse1359-1020-Numbers
• File: Itse1359-1020.htm
• Published: 10/14/14
• Revised: 03/26/15
Disclaimers:

Financial : Although the Connexions site makes it possible for you to download a PDF file for thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

I also want you to know that, I receive no financial compensation from the Connexions website even if you purchase the PDF version of the module.

In the past, unknown individuals have copied my modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing me as the author. Ineither receive compensation for those sales nor do I know who does receive compensation. If you purchase such a book, please beaware that it is a copy of a module that is freely available on cnx.org and that it was made and published withoutmy prior knowledge.

Affiliation : I am a professor of Computer Information Technology at Austin Community College in Austin, TX.

-end-

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