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ADAM CLEMENTS SME 430 Discussion Post #1 1/19/2010

Read Sketch 1 (Keeping Count - Writing Whole Numbers - p. 61-66) and Sketch 2 (Reading and

Writing Arithmetic - Where the Symbols Came From - p. 67-70) before responding to the

following prompts. Submit your responses as a post to this discussion forum.

1. Think about the number system we are using right now. Write down three to fiveproperties of our number system. For example, we are using 10 symbols to make up all

the numbers (0, 1, 2, 3,...9). Consider the in-class activity and the readings for this week.

Our number system is a base 10 system. It uses place value, thus is a positional number system meaning that the position of

the symbols determines the value.

The numbers (0, 1, 2, 3 9) are called digits. Each number represents a point on the number line. Any number can also be expressed in words.

Compare our number system with two other number systems used in the history of

mathematics. In your opinion, what advantages and disadvantages do you see with the

different number systems that have been presented.

Our Current Number System Ancient Egypt Babylonian

Advantages:

Good for computationThe symbol represents the

number. There is no

counting of lines or dots

involved.Can write a large number in

a small amount of space.

Disadvantages:

Its very easy to change thenumber just by adding a 0

or another number to the

end.

Advantages:

Few symbols to rememberOrder of symbols doesnt

matter easy to write

Disadvantages:Involves counting the

number of symbols for

each place value.

Order of symbols doesntmatter can get confusing

to count

Limited symbols to denotemuch larger numbers

million, trillion, etc)

Drawings could bedescribed as a bit complex

Advantages:

Only two symbols used.Easy to make.

Disadvantages:

Uses a base multiplicationof 60. This can getconfusing and involves

computation just to figure

out what number is being

represented.

Involves using spaces todenote two groups. Hard

to tell if it is a space or

not. This gets confusing.

Involves counting thesymbols to determine how

many they represent

In your opinion what are important characteristics for a number system to have?

Consistency in symbols Minimal symbols to represent the numbers The number can be easily identified without counting or computing computations


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2. Consider the following definition of positional number systems... "positional notation orplace-value notation is a numeral system in which each position is related to the next by a

constant multiplier, a common ratio, called the base (or radix) of that numeral system".

According to this definition, which of the number systems we have looked at are positional

and which ones are not? Explain your choices.

Positional number systems

Babyloniano For each single combination value was multiplied by an appropriate power of 60.

This is a base 60 number system. The order and position of the symbols

determined its value.

Mayao The system is essentially based on twenty, excepts for the peculiar use of 18. The

lowest group represents a single unit, the second group was multiplied by 20, the

third by 18*20, the fourth by 18*202, the fifth by 18*20

3and so on. Also, the

position of the symbol determines the value.

Hindu-Arabic (our current system)o Each position increases by a ratio of 10. This is a base ten number system. Also,the position of the digit determines the value.

Not positional number systems

Ancient Egyptiano Each symbol increases by a ratio of 10. This is a base ten number system,

however, the order of the symbols can be mixed up and thus the position of the

symbols does not affect its value.

Roman Numerals and Greeko These systems do not hold place value. The position of each symbol does not

denote its value.

3. According to the reading, the use of symbols in representing arithmetic operations is afairly recent adoption. Why do you think the use of symbols has caught on?

Symbols can be universal. The fact that math is universal is a very important anduseful aspect of it. Thus, having the same symbols for math across the world is very

useful for sharing information.

What reason do you think prevented symbolic operations from being adopted sooner?

I think that since in the past communication between different cultures was verylimited because of limited means of travel, different groups of people were coming upwith different ways of expressing the same things. Thus when they were able to

communicate, each group was hesitant to change or adapt to something different.

However when they realized that symbols would cause less confusion among

different groups that words, the change to symbols began to occur.


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Do you think that you can use the standard algorithm for addition or multiplication we

are using today in other number systems. Why or why not? If yes, how?

I think it is possible, but it would be very challenging. First, computing the differentnumbers would be the first task. Actually figuring out what number the symbols

represent. Then doing the computation simply based on those numbers. Additionwould be easy for a system like Egyptian because you simply add up the different

pictures together. However, if you had to carry or exchange a group of more

than 10, this would get confusing. Systems like the Roman numerals would however

be very difficult to do computations. Without translating most of the other systems,

it would be extremely difficult to do computations. Often you are having to do

computations simply to figure out what the number is, then adding or multiplying two

of these numbers together would get very difficult and confusing.

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