 # 1.2 Number Bases, SPM Paper 1 (Short Questions)

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

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.