1. CHAPTER 5 SEC 3 Calculating in Other Bases

2. Bases The Babylonian had a base of 60. The Mayan system used a base of 20. The Hindu-Arabic we use today is in base 10.

3. What other bases do we use everyday ? Base 2 (the binary)  The use of computers and cell phone.  The only numbers that are used are zeros and ones.

4. Other bases Base 2  1, 10 2, 11 2, 100 2, 101 2, 110 2, … Base 5  1, 2, 3, 4, 10 5, 11 5, 12 5, 13 5, 14 5, 20 5, … How about base 7?

5. Each number has a place holder, for example given the number 485 9. The subscript 9 is the base that we will have to work in. The 5 is the ones, the 8 is the tens, and the 4 is in the hundreds. What we want to do is to expand,  4x9 2 + 8x9 1 + 5x9 0  = 4x81 +72+5 = 324+77 = 401

6. What we are going to be trying to do is to convert a different base into base 10. For example, covert 24, 456 7 into base- 10.

7. Hindu-Arabic into a different base. Write 768 into base 5.

8. Now we read the remainders in reverse order. Therefore our number is 10,344 5.

9. Addition

10. Try these problems 553 6 + 245 6 11242 6 1325 6 – 453 6 4432 6

11. Multiplication