JSS3: MATHEMATICS  1ST TERM

Binary Number System I  Week 15 Topics1 Quiz

Binary Number System II  Week 26 Topics1 Quiz

Word Problems I  Week 34 Topics1 Quiz

Word Problems with Fractions II  Week 41 Topic1 Quiz

Factorisation I  Week 54 Topics1 Quiz

Factorisation II  Week 63 Topics1 Quiz

Factorisation III  Week 73 Topics1 Quiz

Substitution & Change of Subject of Formulae  Week 82 Topics1 Quiz

Simple Equations Involving Fractions  Week 93 Topics1 Quiz

Word Problems  Week 101 Topic1 Quiz
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Number Bases
The usual system of counting in recent times is called the decimal or denary system.
This system enables us to write small or large numbers using a combination of digits.
Example:Â 6843, Â 614.35
Each digit in a number has a place value
For example,Â 8321 means 8 thousands,Â 3 hundreds, 2 tens, 1 unit
This can be shown using powers of 10 as follows
This can be written in expanded notation as
8 x 10^{3}Â + 3 x 10^{2} + 2 x 10^{1} + 1 x 10^{0}
8 x 1000 + 3 x 100 + 2 x 10 + 1 x 1
8000 + 300 + 20 + 1
Also, the decimal fractionÂ 0.532 means 5 tenths,Â 3 hundredths, 2 thousandthsÂ
i.e. 0.532 = 5 x 10^{1} + 3 x 10^{2} + 2 x 10^{3}
Numbers in base 10 are usually written without the subscript ten or 10
431_{ten} is simply written as 431.
Apart from base 10, numbers are counted in other bases such as base two, base five, base seven, base eight etc.
Note: Numbers in other bases are also written in expanded notation.
For example,Â
158 in base five is
158 = 1 x 5^{2} + 5 x 5^{1} + 8 x 5^{0}
= 1 x 25 + 5 x 5 + 8 x 1
Any number raised to the power 0 = 1 so in the above example 5^{0} = 1.
Example
Write the following numbers in expanded form.
a. 5314.23Â
b. 31506_{eight}Â
c. 232.01_{five}Â
d. 5097_{ten}
e. 163.07_{ten}
Solution
a. 5314.23Â meansÂ 5314.23 _{ten}
5 x 10^{3} + 3 x 10^{2} + 1 x 10^{1} + 4 x 10^{0 }+ 2 x 10^{1} + 3 x 10^{2}
b. 31506_{eight}Â =Â 3 x 8^{4} + 1 x 8^{3} + 5 x 8^{2} + 0 x 8^{1} + 6 x 8^{0}
c. 232.01_{five}Â = 2 x 5^{2} + 3 x 5^{1} + 2 x 5^{0} + 0 x 5^{1} + 1 x 5^{2}
d. 5097_{ten} = 5 x 10^{3} + 0 x 10^{2} + 9 x 10^{1} + 7 x 10^{0}
e. 163.07_{ten} = 1 x 10^{2} + 6 x 10^{1} + 3 x 10^{0} + 0 x 10^{1} + 7 x 10^{2}
It was fun.
Answers
A. 5000+300+ 10+4+0.2+0.03
=5314.23
It was fun.
It was interesting and it helps for people who fully didn’t understand what was been taught in the class