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

 Page 6 / 6

## 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-

what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!