Question 1:
Solution:
Express 2058 as a number of base five.
Solution:
2058 = 2 × 82 + 0 × 81+ 5 × 80 = 13310
Question 2:
Solution:
State the value of the digit 6 in the number 16238, in base ten.
Solution:
Identify the place value of each digit in the number first.
1 |
6 |
2 |
3 |
|
Place Value |
83 |
82 |
81 |
80 |
Value of the digit 6
= 6 × 82
= 384
Question 3:
Solution:
Given 3 × 53 + 4 × 52 + 5p = 34205, find the value of p.
34205 = 3 × 53 + 4 × 52+ 2 × 51 + 0 × 50
34205 = 3 × 53 + 4 × 52+ 5p+ 0
5p = 2 × 51
5p = 10
p = 2
Question 4:
Solution:
Convert 4 × 84 + 2 × 82 + 4 to a number in base eight.
84 |
83 |
82 |
81 |
80 |
4 |
0 |
2 |
0 |
48 |
Answer = 402048
Question 5:
Solution:
What is the value of the digit 3, in base ten, in the number 43155?
Identify the place value of each digit in the number first.
4 |
3 |
1 |
5 |
|
Place Value |
53 |
52 |
51 |
50 |
Value of the digit 3
= 3 × 52
= 75Question 6:
Solution:
Express 5(52 + 2) as a number in base 5.
Step 1: Expand 5(52 + 2) first.
Step 2: write 5(52 + 2) in expanded notation for base 5.
5(52 + 2)
= 53 + 2 × 5
= 1 × 53 + 0 × 52 + 2 × 51+ 0 × 50
= 10205
53 |
52 |
51 |
50 |
1 |
0 |
2 |
05 |
Question 7:
Solution:
1101102 – 111012 =
Alternatively, use a scientific calculator to get the answer directly.