1In basefive numeration 3 flats 2 longs and 4 units are reco

1.In base-five numeration, 3 flats, 2 longs, and 4 units are recorded by the numeral 324five. Sketch the base pieces for each of the following numerals, and determine the total number of units in each collection. a.1304five b.221five c.213five d.1023five

2. Starting with the unit, sketch the first four base-three pieces. What is the minimal collection of base-three pieces for 16 units? What is the total number of units represented by 2112three (2 long-flats, 1 flat, 1 long, 2 units)?

Solution

1.a) 1304 five = 1*5³ + 3 * 5² + 0* 5¹ + 4* 5⁰ = 125 + 75 + 4 = 204 units are present in 1304 five

b) 221 five = 2* 5² + 2 * 5¹ + 1 * 5⁰ = 50 + 10 +1 = 61 units are present

c) 213 five = 2* 5² + 1 * 5¹ + 3 * 5⁰ = 50 + 5 + 3 = 58 units are present

d) 1023 five = 1 * 5³ + 0 * 5² + 2* 5¹ + 3 * 5⁰ = 125 + 10 + 3 = 138 units are present;

2. The minimal colection for base 3 pieces for 16 units is 1 * 3² + 1 * 3¹ + 4 * 3⁰ = 114 ;

( or ) 1 * 3² + 2 * 3¹ + 1 * 3⁰ = 121 ;

the total number of units 2112 represents = 2 * 3³ + 1 * 3² + 1 * 3¹ + 2 * 3⁰ = 54 + 9+3 +2 = 68 units