2. A martianproblem WhenthefirstMartiantovisitEarthattended a highschool algebra class, he watchedtheteacher show thattheonlysolution of theequation5x2-50x+125=0isx=5. “Howstrange”, thougththeMartian. “OnMars, x=5is a solution of thisequation, butthereisalsoanothersolution.” IfMartianshave more fingersthanhumanshave, howmanyfingers do Martianshave? Bonnie Averbach & OrinChein
3. Firstreview – Positionalnotation Ten symbols are required by our number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 24= 204= 315= 45.2= The relative position to the decimal point indicates the “place value” of the digit 3= 3x1 =3x100 30= 3x10 =3x101 300= 3x100 =3x102 0.3= 3 /10 =3x10-1
4. First review – Other bases What if we have a number system with only two different symbols? (110)two= (110)three= (110)ten= (110)four= 0, 1 So, the number 1101 in base two represents: 1 x23 + How many symbols do we need in base three? And the number 120 represents …
5. First review – Changing bases (201)three=2x32+0x3+1=(19)ten (185)ten=(???)three = 2 x 81 + (185-162) = 2 x 81 + 23 = 2 x 81 + 2 x 9 +(23-18) = 2 x 81 + 2 x 9 + 5 = 2 x 81 + 2 x 9 + 3 +2 = 2 x 34+ 0 x 33 + +2 x 32+ 1 x 31 + 2 x 30 = (20212)three (10011)two= =(19)ten (1101)two= (1001)seven= (3.5)six= (T81)eleven= (5403)six= Convert (2087)teninto each of the following bases: 2, 3, 6, 7, 12
