Converting Between Bases Do Now: Please arrange yourselves in a large semicircle. Opening Question: Suppose instead of base 10 blocks we wanted to use base 5 blocks. What would they look like? Try to represent 14 by drawing base 5 blocks. Part I: Game Time! Bizz Buzz in Base 5 Bizz Buzz is a counting game where the rule is that you cannot say the number of the base you are playing in. If we play Bizz-Buzz in base 5, we cannot say five. We count 1, 2, 3, 4, bizz, 1, 2, 3, 4, bizz bizz, 1, 2, 3, 4, bizz bizz bizz, etc. Instead of saying bizz five times, we say buzz. Let's play a couple of rounds... feel free to take notes in the space below. 1. How to we represent 14 in Bizz-Buzz Base 5? We can also write the number with a subscript of 5, to show that we are in base 5: 24s ] (A number without a subscript is assumed to be in base 10) 2. How would we represent 28 in Bizz-Buzz base 5? Also write the number using the subscript notation. 3. How would we represent 52 in Bizz-Buzz base 5? Also write the number using the subscript notation. Converting Between Bases Group Members: List the names of your group mates below. Part Il: Base 5 blocks (fill in the table below) Cubes Flats Rods Units One hundred and Twenty | Twenty fives Fives fives Five rods make one flat. Five cubes make one rod. Five flats make one cube. 125 25 1. For each number below (i) use base 5 blocks to represent the number (ii) fill in the base 5 table and (iii) write the number using the subscript notation. a) 14 b) 28 c) 52 d) 117 Converting Between Bases 2. In the space below, describe a procedure for converting a number in base 10 into base 5. 3. Test out the procedure on the following numbers: a) 17 b) 34 c)260 4. Now, suppose we wanted to convert 315 to base ten. Place each digit in its correct position in the base five table below. Then rewrite it in expanded form. 50 | | Multiplier | Exponent 51 5. Convert 1425 to base ten. Use a base 5 table, or base 5 blocks to help you. 6. Convert 2345 in base ten. Use a base 5 table, or base 5 blocks to help you. 7. In the space below, describe a procedure for converting a number in base 5 into base 10. Converting Between Bases 8. Test out your procedure on the following numbers: b) 115 b) 2045 c)12115 Part III: Converting To/From Other Bases 1. For the following exercises convert from the indicated base to base 10. a) 147 b) 2067 c) 14012 d) 51312 e) 10112 f) 10102 2. For the following exercises convert from base 10 to the indicated base. a) 207 to base 7 b) 1314 to base 7 c) 38 to base 12 d) 163 to base 12 e) 85 to base 2 f) 258 to base 2 3. Which direction do you think is easier? Converting from base 10 to another base, or converting from another base to base 10. Why