Archive for: August 2008

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How do you symbolize different bases? Is there a way that mathematicians write “base 2″ for example, without having to write out the words?

There are several ways that bases can be symbolized. The two most common are simply to subscript the number of the base to the right and down of the number, like this:

101₂

That lets you know that we are dealing with the number 101 (base two), not the number 101 (base ten). 101 in base two would be 5 in base ten.

Sometimes the base is written out as a word in the subscript, like:

101_two

Depending on the context, one may be more convenient than the other, but both are accepted. It is probably best to use the written out word in subscript, because there are other uses for a subscripted number to the right of a number in math. Using the written out word, as in:

423_six

makes unambiguously clear that you are only talking about a base.

Anyone care to have a shot at what 423_six would be in base 10? Leave it in a comment.

Tags: base notation , how to write bases

This short lesson is a continuation of the posts at:

What is a Base? and
How to change base 2 numbers into base 10

In those lessons, we talked about what bases are, what they’re used for, and how to change numbers from base 10 to base 2 (easy!)

It’s even easier to change numbers from base 2 into base 10.

When you read a number in base 2,  you simply have to add the columns together that have a 1 in them, and ignore the columns with a 0 in them. 

In the number 111(base 2) there is a 1 in the fours, twos, and ones columns. Simply add 4, 2, and 1 to get the base 10 value, which is 7. 

The number 10110 has a 1 in the sixteens column, another in the fours column, and another in the twos column. So add 16 + 4 + 2, to give you 22, base 10.

You have to admit that’s pretty easy. 

What would the number 110101 (base 2) be, in base 10?

Answer it in a comment, if you like.

Tags: convert base 2 to base 10

A number is a concept that we have for some value. For example, hold out four fingers. You can conceive of the number four, you know how many are there. That is the number - more or less the concept you have in your mind.

A numeral is a name or a symbol for that concept. The symbol may be a 4 (in base 10) or a 100 (in base 2) or IV (if you are using Roman numerals) or |||| if you are using tally marks, etc. All of those symbols look different on paper. But the concept in your mind remains the same.

So a number may be expressed many different ways, using different numerals. But a numeral will always represent the same number, as long as you know what system (base, Roman, tally, etc.) you are using.

It might help to think of it like languages. For example, a “book” is a word for that thing you read, with many pages. In German, it’s a “Buch,” in French it’s a “libre,” in Spanish it’s a “libro,” and in Vulcan it’s, well, I don’t know what it is in Vulcan, but you get the picture. They are all different words for the same Idea. The book is the actual object, but “book,” “Buch,” “livre” and “libro” are simply words, or names for the object.

So you might consider numbers to be the Ideas, and numerals to be the names for the Ideas.

Of course, as always, there are more in-depth ways to look at this issue, but the above should give you a good, working basis to explore further, if you wish.

I hope this gave you something to think about, 

Your pal, 

Brian

Tags: numbers , numerals

A reader recently sent in this problem:

Help, how do you solve this???

The area of a rectangle is 624cm².
The base is 8 less than 5 times the height.
What is the perimeter?

I can not find out how to do it on line. I have a number of similar problems to solve
thanks.

- A. Reader.

Professor Homunculus replies:

Hi, Reader,

I must say that it is a good thing that it is not taught online. Specific problems should never be shown online. That would be show-and-tell, not teaching.

What you need to learn is the concepts behind the problems, then you’ll be able to crack all problems that are similar. One of the concepts is a very interesting and important part of algebra. 

Here’s a way to start figuring out how to solve your problem:

(more…)

Tags: area , base , geometry , height , perimeter , rectangles , word problems quadratic equation