Number Bases Short Questions (Question 1 – 7)


Question 1:
Express 2058 as a number of base five.

Solution:

2058 = 2 × 82 + 0 × 81+ 5 × 80 = 13310
 



Question 2:
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:
Given 3 × 53 + 4 × 52 + 5p = 34205, find the value of p.
 
Solution:
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:
Convert 4 × 84 + 2 × 82 + 4 to a number in base eight.
 
Solution:
84
83
82
81
80
4
0
2
0
48
Answer = 402048



Question 5:
What is the value of the digit 3, in base ten, in the number 43155?
 
Solution:
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
= 75



Question 6:
Express 5(52 + 2) as a number in base 5.
 
Solution:
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:
1101102 – 111012 =
 
Solution:

Alternatively, use a scientific calculator to get the answer directly.

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