# Exploring the Decimal System in Math

• trini
In summary, base 10 is the most popular because it has the most finite answers within a range. Other systems have more infinite answers.
trini
Ok so i was thinking about it recently, why do we use the decimal system as opposed to other counting systems in math? is there some distinct advantage in using decimal over other systems?

Because we have ten fingers.

that's all? that seems quite illogical as there appear to me to be many more irrational decimal numbers than there are in, say, base 6 number systems(senary)

trini said:
that's all? that seems quite illogical as there appear to me to be many more irrational decimal numbers than there are in, say, base 6 number systems(senary)

There are exactly the same number of irrational numbers in base 6. In fact whether a number is irrational or not does not depend on the base. The choice isn't that important for most uses so we just stick with what's popular. Base 2, 8 and 16 are also pretty popular bases (especially in computer science).

The existing numeral system coalesced more than a 1000 years ago, at the time when numbers were mostly used for finger counting. Finger counting application makes systems which are based on numbers 5 and 10 preferable over all others. Once a convention like that is universally accepted, it's very hard to replace it, even in the face of major advantages of other conventions (the use of imperial units like foot and pound in the US and the UK is a good example).

hamster143 said:
... (the use of imperial units like foot and pound in the US and the UK is a good example).
You think we count in base 10 because we are too proud and bloody-headed to change?

The United States can't even switch to using the metric system for weights and measures. It would take a major miracle to change our ordinary number system to ther than decimal.

sorry perhaps i should have said recurring numbers, as for example, 1/3 to base 6 = 0.2

to compare systems, i look at the number of finite vs. infinite answers within a range, so for example, in a case of 1/n, where n is an integer, base 6 carries less infinite answers than base 10 over wide ranges.

yes i understand your point, and it would be very difficult to see such a thing happening without some MAJOR application, especially given the intuitiveness of the finger based system in teaching, as you pointed out though, it is used where useful(eg computer science.)

Another question, does changing base affect the shapes of functions in any way? for example, in the case of plotting a number series, would the series have a different shape if plotted in a system other than decimal?

trini said:
sorry perhaps i should have said recurring numbers, as for example, 1/3 to base 6 = 0.2

to compare systems, i look at the number of finite vs. infinite answers within a range, so for example, in a case of 1/n, where n is an integer, base 6 carries less infinite answers than base 10 over wide ranges.

It's easy to see that you can write down more fractions with, say, two base 10 digits than with two base 6 digits.

why? you can write the same amount of fractions, except, for eg, instead of saying 1/9 (decimal) you would say 1 / 13 ( senary) the only difference would be u have to use more digits as far as i can see.

There are, after all, organized groups supporting, say, base 12 and even some people plugging for base e!

As rasmhop said, there are exactly the same number of irrationals in any numeration system. The distinction between irrational and rational numbers is independent of the numeration system. As for "terminating" and "repeating" decimals, there really isn't that much difference in difficulty of working with them.

I vote for hexadecimal! It is so much easier to do a binary search in hexadecimal than decimal and it is more concise than binary or octal.

DaleSpam said:
I vote for hexadecimal! It is so much easier to do a binary search in hexadecimal than decimal and it is more concise than binary or octal.
Nah. Doesn't support thirds. 12 is divisible by 2,3,4 and 6.

The way to go is to teach the general population to use hexadecimal, since it's already universal as an internal representation in computers, and to popularize the () notation:

1/2 = 0.8
1/3 = 0.(5)
1/4 = 0.4
1/5 = 0.(3)
1/6 = 0.2(A)
1/7 = 0.(249)
1/8 = 0.2
1/9 = 0.(1C7)
1/1234 = 0.00(351BCC8D11D756B763FE57219B9771454A44E00D46F3234475D5ADD8FF95C866E5DC515291380)To improve usability, we can replace () with a second dot:

1/6 = 0.2.A
1/9 = 0..1C7

I am torn between base 12 and hexadecimal. Both have nice features, the number of prime divisors for 12 is handy, as is the correspondence with binary for base 16.

What ever 10 is the worst of the lot. With the biggest nastiness being the inability to precisely convert .1 (decimal) to binary.

Unfortunately there is no hope of ever changing, all this is just nerdy pipe dreams.

I prefer Slot Machine Arithmetic. See http://mensanator.com/rotanasnem/cherries/cherries.htm"

Last edited by a moderator:
hamster143 said:
Because we have ten fingers.

I was reading about the advantages of the base 8 system a few weeks ago, and the book I was reading from mentioned something about some ancient Central American civilization using the base 8 system. The author asked mathematicians about why this might be advantageous, and they gave answers like "8 has more factors than 10," "8 is a power of 2," etc. However, when he asked a group of children, they said that this civilization was just counting the spaces between their fingers; I thought it was pretty interesting.

pzona said:
I was reading about the advantages of the base 8 system a few weeks ago, and the book I was reading from mentioned something about some ancient Central American civilization using the base 8 system. The author asked mathematicians about why this might be advantageous, and they gave answers like "8 has more factors than 10," "8 is a power of 2," etc. However, when he asked a group of children, they said that this civilization was just counting the spaces between their fingers; I thought it was pretty interesting.

Interesting. There are also some languages that use base 12 because of the number of phalanges on four "main" fingers. And there's a couple of tribes in New Guinea that use 27, and no one knows for sure how that came about. But most cultures, from Chinese to Greeks to Maya, came up with different varieties of base 10 independently of each other.

## What is the decimal system in math?

The decimal system, also known as the base 10 system, is a way of representing numbers using ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and place values. This system is used in most modern cultures and is the foundation of arithmetic operations like addition, subtraction, multiplication, and division.

## How does the decimal system work?

The decimal system works by using place values to represent different magnitudes of numbers. Each place value is ten times larger than the one to its right. For example, in the number 123, the "1" represents 100, the "2" represents 20, and the "3" represents 3. This system allows us to easily represent and manipulate large numbers.

## What are some real-life applications of the decimal system?

The decimal system is used in many real-life applications, such as representing money, measuring distance and weight, and telling time. It is also used in science and engineering to represent precise measurements and calculations.

## Why is understanding the decimal system important?

Understanding the decimal system is important because it is the foundation of our number system and is used in many aspects of our daily lives. It also helps develop critical thinking and problem-solving skills, as well as preparing students for more advanced mathematical concepts.

## How can I improve my understanding of the decimal system?

To improve your understanding of the decimal system, you can practice using it in everyday activities, such as counting money or measuring ingredients for a recipe. You can also seek out additional resources, such as worksheets or online tutorials, to reinforce your understanding of the concept.

• Linear and Abstract Algebra
Replies
19
Views
742
• Introductory Physics Homework Help
Replies
9
Views
326
• General Math
Replies
7
Views
1K
• Computing and Technology
Replies
4
Views
1K
• General Discussion
Replies
53
Views
3K
• Linear and Abstract Algebra
Replies
3
Views
1K
• General Math
Replies
10
Views
942
• Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
32
Views
2K
• General Math
Replies
3
Views
2K