Question

1. questions (only complete this problem if lesson 1.6 is read) a. what would it mean if you were told a number was written in a base - 5 place - value system? b. how many digits would you need to write a number in a base - 5 place - value system? hint: think through what you learned about the base - 10 (decimal), base - 2 (binary), and base - 16 (hexadecimal) systems. a. 1100 > 1000 b. 10000 > 1000 c. 1010 < 1011 d. 1111 - 1111

Explanation:

Step1: Recall base - 5 system digits

In base - 5 system, digits range from 0 to 4. So there are 5 digits.

Step2: Interpret base - 5 number meaning

A number written in base - 5 place - value system means that each digit's value is determined by its position and the base 5. For example, in the number \(abc\) (in base - 5), its value is \(a\times5^{2}+b\times5^{1}+c\times5^{0}\), where \(a,b,c\in\{0,1,2,3,4\}\).

Answer:

a. It means the number is represented using digits 0 - 4 and each digit's value depends on its position with base 5.
b. 5 digits (0, 1, 2, 3, 4)