2. NUMERATION SYSTEMS IN BASES OTHER THAN 10 Pamela Leutwyler

3. Remember – a numeration system is a system for NAMING numbers. As you change from one system to another the number does not change only its name changes

4. COUNT THE CAMELS

5. Base 10

6. 1 3 10

7. Base 10 1 3 10

8. Base 10Base 7 1 3 10 1 6 7

9. Base 10Base 7 1 3 10 1 6 7

10. Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5

11. Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5

12. Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 4 1 3 ?

13. Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 1 1 3 1

14. Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 1 1 3 1

15. Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 1 1 3 1 2 3 5 = _______ 10 1 3 10 = _______ 3

16. Imagine a base 4 pebble board It does not matter what pile you look at – The same rule always holds. 4 pebbles in this pile equals 4 pebbles in this pile equals 4 pebbles in this pile equals 1 pebble in this pile equals 1 pebble in this pile equals 1 pebble in this pile equals

17. We think and compute in the base 10. BASE 10 is the DEFAULT BASE We will learn algorithms for converting numerals: 1.) TO THE BASE 10 FROM ANOTHER BASE 2.) TO ANOTHER BASE FROM THE BASE 10

18. converting TO the base 10: 2 1 4 = _________ 10 base 4

19. converting TO the base 10: 2 1 4 = _________ 10 base 4 2  4 + 1 9

20. converting TO the base 10: 1 1 1 2 = _________ 10 base 2 1  2 2 + 1  2 + 1 7

21. 1 2 3 2 4 = ________ 10 4343 4242 41 ( 1  4 3 ) + ( 2  4 2 ) + ( 3  4 ) + ( 2  1 ) 64 + 32 + 12 + 2 1 1 0 4040 4141

22. converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1

23. converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1 3 3 - 2

24. converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1 3 3 - 2

25. converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1 3 3 - 2 3 1 - 0 1 0 2 1