1. Number Bases Ancient number systems Clock math

2. First some back ground Our number system is in base 10, that means we have 10 symbols we use before we “start over” 0,1,2,3,4,5,6,7,8,9 10 is the first number that contains 2 symbols.

3. Think about a clock Now a clock while written in base 10 numbers works in a base 12 system. If we used military time we would say that 1:00 pm is 13:00. Because we don’t use military time, we say 1:00 pm. So 1pm and 13:00 really represent the same thing This means that 1 is equivalent to 13 when we are using out base 12 number system. This also means that 1 = 13, 25, 37… so on.

4. Not only 10 and 12 We also use base 60 for time (60 seconds in a min, 60 min in an hour) Base 2 (binary) There are infinitely many bases, but we are only going to play with ones between base 2 and base 10 today.

5. PAUSE, lets review exponents

6. Binary (base 2) Ok so with binary we are only going to have 2 digits we use. 0 and 1 So if I want to write the 2 in binary…. I only have 0 and 1 so how am I going to do it? Well we have already used 0 and 1 so now we have to combine the two digits. 10, 3 would be represented like this : 11

7. PAUSE: Lets make a table n 0 1 2 3 4 5 6

8. How to figure out a number in binary

9. Lets try it

10. Lets convert it to binary

11. On your paper: Convert the following numbers to Binary 5 8 9 20 100

12. Lets try a different base Lets try base 3

13. PAUSE Lets make a table: n 0 1 2 3 4 5 6

14. Lets try a different base

15. On your paper On your paper convert the following numbers into base 3. 6 8 13 27 100

16. Lets play Now that you have an idea how bases work pick a base between 1 and 10 (not 2 or 3) and write all the numbers between 0 and 10 in that base.

17. A little bit of History It was not until the 15 th century that Europe started using the number symbols we use today. Our number system is called the Hindu-Arabic system Tally marks used to be one of the main ways that people wrote numbers but, that takes a lot of time.

18. Number systems around the world Natives of Queensland used base 2 Modern south American tribes have a base 5 system Babylonians used base 60 Mayans used two different number systems, one for common people and one for priests. The priests used a base 20/360 it had to do with the number of days in a year and was very complex The common people used a base 20 system

19. Writing numbers in Mayan There are only 5 symbols in the common Mayan numerical system and work some what like roman numerals. Numbers were read from bottom to top and remember in base 20

20. Reading numbers If numbers are read from the bottom up, with the bottom being the ones place this number can be read as 13 in the ones place and 3 in the 20’s place. So in our base 10 this would be 73

21. Reading numbers

22. Reading Numbers

23. Lets go the other way Convert 40 into Mayan numerals. Convert 527 into Mayan numerals.

24. How to add in Mayan If I wanted to add 37 and 29 using Mayan numbers what would it look like?

25. How to add in Mayan First lets draw our two numbers in Mayan 37 will look like this 27 will look like this Now we put them next to each other like this

26. How to add in Mayan So we have our numbers written next to each other Now we take all the symbols from both numbers and put them into a single set of places. Now we need to carry just like we would do normally.

27. How to add in Mayan We start at the bottom, currently we have 6 dots but if you remember how the numbers were written we max out at 4. 5 dots = 1 bar This means we need to convert 5 of the dots into a bar and we are left with just one dot and 5 bars. Now remember that 4 bars equals one dot in the higher level (4 bars = 20, 1 dot in a higher level equals 20). So we need to take 4 bars and make it a dot in the level higher. This leaves us with 1 dot and 1 bar in the bottom.

28. Adding in Mayan So our final addend should look like this

29. Adding in Mayan Lets try another problem. Using Mayan symbols add 58 and 33