Egyptian numeration system

The Egyptian numeration system evolved around 3400 BCE. It uses special symbols to represent numbers that are power of 10

You can see the symbols below. Study them carefully before looking at the examples to follow!

Notice that for number greater than 10, this numeration system will require fewer symbols than theTally numeration system

Study carefully the following examples:

245 can be represented as:

2008 can be represented as:

2,320,111 can be represented as:

By now, you should have noticed that this system is additive. However, addition can quickly become a pain in the neck if you are doing addition

You may need many symbols to express an addition problem

Here is an example of addition with Egyptian numerals:

290 + 820 = 1,110

Hindu-Arabic numeration systemThe Hindu-Arabic numeration system evolved around A.D. 800. It is basically the numeration system that is widely used today.

The following lists 4 main attributes of this numeration systemFirst, it uses 10 digits or symbols that can be used in combination to represent all possible numbersThe digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.Second, it groups by tens, probably because we have 10 digits on our two hands. Interestingly enough, the word digit literally means finger or toesIn the Hindu-Arabic numeration system, ten ones are replaced by one ten, ten tens are replaced by one hundred, ten hundreds are replaced by one thousand,10 one thousand are replaced by 10 thousands, and so forth...Third, it uses a place value. starting from right to left, the first number represents how many ones there are the second number represents how many tens there are the third number represents how many hundreds there are the fourth number represents how many thousands there are and so on...

For example, in the numeral 4687, there are 7 ones, 8 tens, 6 hundreds, and 4 thousands

Finally, the system is additive and multiplicative. The value of a numeral is found by multiplying each place value by its corresponding digit and then adding the resulting products

Place values: thousand hundred ten one

Digits 4 6 8 7

Numeral valueis equal to 4 1000 + 6 100 + 8 10 + 7 1 = 4000 + 600 + 80 + 7 = 4687

Notice that the Hindu-Arabic numeration system require requires fewer symbols to represent numbers as opposed to other numeration system

Each Hindu-Arabic numeral has a word name. Here is short list:

0: Zero 10: Ten

1: One 11: Eleven

2: Two 15: Fifteen

3: Three 20: Twenty

4: Four 30: Thirty-four

5: Five 40: Fourty

6: Six 100: One hundred

7: Seven 590: Five hundred seventy

8: Eight 5083: Five thousand eighty-three

9: Nine 56000: Fifty-six thousand

Numbers from 1 through 12 have unique names

Numbers from 13 through 19 have "teens" as ending and the ending is blended with names for numbers from 4 through 9

For numbers from 20 through 99, the tens place is named first followed by a number from 1 through 10

Numbers from 100 through 999 are combinations of hundreds and previous names

Tally numeration systemThe tally numeration system is probably the simplest of all numeration systems ever used.

It makes use of single strokes to represent object being counted. One stroke is used for each object

The following shows how we can use stroke(s) to represent the count for 1, 2, or 3 squares

Although one advantage is simplicity, there are two disadvantages.

First, large number will require an aweful lots of strokes.

Second, it will be somewhat difficult to real such large number

For example, can you tell what number is represented by the tally marks below?

I know what you are doing right now. You are using your finger to count the strokes

However, would you be able to do that without confusing yourself or losing your place if there were 50 strokes?

If you did not lose your place, you must have counted 20 strokes

However, the introduction of grouping made it a lot easier to read numbers

In this case, we place a fifth tally mark across every four to make a group of 5

The number shown above will be represented as follow:

Did you notice that you were able to find the number a lot faster?

Basically, that is all there is to this numeration system.Today, this numeration system is used a lot in stastistics.

Roman numeration systemThe Roman numeration system evolved around 500 BCE. Just like other anscient numeration systems, it uses special symbols to represent numbers.

The basic Roman numerals are the followings. Study them and memorise them if you can. It could become handy one day

Any other roman numerals are found by combining these basic numerals

Examples:

1) 154 is equivalent to CLIIII in Roman numerals

2) 1492 is equivalent to MCCCCLXXXXII in Roman numerals

3) 3495 is equivalent to MMMCCCCLXXXXV in Roman numerals

Over time, two useful attributes were introduced that made the Roman numeration system very useful and efficient

The first one is thesubractive principle

With the subtractive principle, Roman numerals can be combined or paired so that when reading from left to right, the values of the symbols in any pair increase.

The value of the new pair is:

bigger number in the pair smaller number in the pair

For instance, I can pair I and V to make IV and the value of this pair will be V I = 5 1 = 4

I can pair C and D to make CD and the value of this pair will be D C = 500 100 = 400

I can pair X and L to make XL and the value of this pair will L X = 50 10 = 40

This subtractive principle will make the writting of examples 1), 2), and 3) a lot simpler

1) CLIIII = CLIV

2) MCCCCLXXXII

Instead of CCCC, we can pair C and D to get CD and CD = 400 as demonstrated above

Also, instead of LXXXX, we can pair X and C to make XC since XC still equal to 90

Replacing CCCC (in bold) by CD, we get:

MCCCCLXXXII = MCDLXXXXII

Replacing LXXXX by XC (in blue), we get:

MCDLXXXXII= MCDXCII

So, instead of using 11 symbols, we can just use 7 to represent the same number

3) MMMCCCCLXXXXV = MMMCDXCV

The second one is themultiplicative principle

Basically, a horizontal bar above any number means 1000 times the number

Examples:

Babylonian numeration system

The Babylonian numeration system was developed between 3000 and 2000 BCE.

It uses only two numerals or symbols, a one and a ten to represent numbers and they looked this these

To represent numbers from 2 to 59, the system was simply additive

Example #1:

5 is written as shown:

12 is written as shown:

Notice how the ones, in this case two ones are shown on the right just like theHindu-Arabic numeration system

45 is written as shown:

For number bigger than 59, the babylonian used a place value system with a base of 60

62 is written as shown:

Notice this time the use of a big space to separate the space value

Without the big space, things look like this:

However, what is that number without this big space? Could it be 2 60 + 1 or 1 602+ 1 60 + 1 or .....???

The babylonians introduced the big space after they became aware of this ambiguity.

The number 4871 could be represented as follow: 3600 + 1260 + 11 = 4871

Even after the big space was introduced to separate place value, the babylonians still faced a more serious problem?

How would they represent the number 60?

Since there was no zero to put in an empty position, the number 60 would thus have the same representation as the number 1

How did they make the difference? All we can say is that the context must have helped them to establish such difference yet the Babylonian numeration system was without a doubt a very ambiguous numeral system

If this had become a major problem, no doubt the babylonians were smart enough to come up with a working system

Cool math tricksThis unit is dedicated to showing you a variety of cool math tricks that will help you tackle some basic math problems with speed and great accuracy.

Multiplying by powers of tenLearn to multiply by powers of ten the easy way with these useful shortcuts tricks

Multiplication by 11Learn how to perform multiplication by 11 in 10 seconds or less with these useful tricks

Squaring numbers ending with fiveWhat if you could square any number two digit number ending in five in 4 seconds or less?

Finger multiplicationEasy, straightforward, and quick multiplication with your fingers!

Number trick with 1089impress your friends with this 1089 trick!