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Question
(a) Convert 110111two to a number in base three
Solution:
First step is to convert the binary number to base 10
110111two = \( \scriptsize 1 \: \times \: 2^5 \: + \: 1 \: \times \: 2^4 \: + \: 0 \: \times \: 2^3 \\ \scriptsize \: + \: 1 \: \times \: 2^2 \: + \: 1 \: \times \: 2^1 \: + \: 1 \: \times \: 2^0 \)
= \( \scriptsize (1 \: \times \: 32) \: + \: (1 \: \times \: 16) \: + \: ( 0 \: \times \: 8) \\ \scriptsize \: + \: (1 \: \times \: 4)\: + \: (1 \: \times \: 2) \: + \: (1 \: \times \: 1) \)
= 32 + 16 + 0 + 4 + 2 + 1
= \( \scriptsize 55_{ten} \)
The next and final step is to convert 55 to base 3
⇒ 110111two = 2001three
Question
Find the value of xº and yº in the figure below.
Solution:
xº = 120º (adjacent pair of sides are)
yº = 60º ( equal property of a kite)
or
yº = 360º – (120xº + 120º + 60º) = 60º
Question
The table below shows how Mrs Ann spent the last month’s salary
| Items | Percentage (%) |
| House Rent | 15 |
| Food | 30 |
| Saving | 25 |
| General Maintenance | 20 |
| Others | 10 |
Represent the above information using a pie chart.
Solution:
| Items | Percentage (%) | Sectoral Angle |
| House Rent | 15 | \( \frac{15}{100} \scriptsize \: \times \: 360^o \\ \scriptsize = 54^o \) |
| Food | 30 | \( \frac{30}{100} \scriptsize \: \times \: 360^o \\ \scriptsize = 108^o \) |
| Saving | 25 | \( \frac{25}{100} \scriptsize \: \times \: 360^o \\ \scriptsize = 90^o \) |
| General Maintenance | 20 | \( \frac{20}{100} \scriptsize \: \times \: 360^o \\ \scriptsize = 72^o \) |
| Others | 10 | \( \frac{10}{100} \scriptsize \: \times \: 360^o \\ \scriptsize = 36^o \) |
Pie Cart
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