# Mathematics - Finite Mathematics - Base-3 System

Suppose that we wished to develop a base three number system to be used in place of either a decimal system or a base two binary system

a-- How many separate symbols would we need in this system? In the binary system, we can get away with only two, 0 and 1. Will this work in a base three system? How would you write the decimal number 2 ?

b-- Write the decimal numbers 6 and 39 in base three form.

c-- What would be a possible use for this system?

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#### Solution Preview

(a) In base 3 system we need the three digits 0, 1 and 2 only and nothing more.

Since 2 is a valid digit in the base 3 system, 2 base 10 = 2 base 3.

(b) We divide 6 by 3 successively until we get zero quotient and write down all the

remainders. This gives starting ...

#### Solution Summary

The expert examines a base-3 system using finite mathematics. How many separate symbols would be needed for the system is determined. Complete, neat and step-by-step solutions are provided.