Question 1:
Solution:
Express 205_{8} as a number of base five.
Solution:
205_{8} = 2 × 8^{2} + 0 × 8^{1}+ 5 × 8^{0} = 133_{10}
_{ }
Question 2:
Solution:
State the value of the digit 6 in the number 1623_{8}, in base ten.
Solution:
Identify the place value of each digit in the number first.
1 
6 
2 
3 

Place Value 
8^{3} 
8^{2} 
8^{1} 
8^{0} 
Value of the digit 6
= 6 × 8^{2}
= 384
Question 3:
Solution:
Given 3 × 5^{3} + 4 × 5^{2} + 5p = 3420_{5}, find the value of p.
3420_{5 }= 3 × 5^{3} + 4 × 5^{2}+ 2 × 5^{1} + 0 × 5^{0}
3420_{5 }= 3 × 5^{3} + 4 × 5^{2}+ 5p+ 0
5p = 2 × 5^{1}
5p = 10
p = 2
Question 4:
Solution:
Convert 4 × 8^{4} + 2 × 8^{2} + 4 to a number in base eight.
8^{4} 
8^{3} 
8^{2} 
8^{1} 
8^{0} 
4 
0 
2 
0 
4_{8} 
Answer = 40204_{8}_{}
Question 5:
Solution:
What is the value of the digit 3, in base ten, in the number 4315_{5}?
Identify the place value of each digit in the number first.
4 
3 
1 
5 

Place Value 
5^{3} 
5^{2} 
5^{1} 
5^{0} 
Value of the digit 3
= 3 × 5^{2}
= 75Question 6:
Solution:
Express 5(5^{2} + 2) as a number in base 5.
Step 1: Expand 5(5^{2} + 2) first.
Step 2: write 5(5^{2} + 2) in expanded notation for base 5.
5(5^{2} + 2)
= 5^{3} + 2 × 5
= 1 × 5^{3} + 0 × 5^{2} + 2 × 5^{1}+ 0 × 5^{0}
= 1020_{5}
5^{3} 
5^{2} 
5^{1} 
5^{0} 
1 
0 
2 
0_{5} 
Question 7:
Solution:
110110_{2} – 11101_{2 }=
Alternatively, use a scientific calculator to get the answer directly.