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GRADE 10
Working with numbers Learning Outcome 1: Number and
Operations in Context
The learner is able to use knowledge ofnumbers and their relationships to investigate
a range of different contexts which includefunctional aspects of personal, business andnational issues
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ASs to be achieved/acquired
Solve problems in various contexts,including financial contexts, by estimatingand calculating accurately using mental,
written and calculator methods whereappropriate, inclusive of: Working with simple formulae Using the relationship between arithmetical
operations (including the communicative,distributive and associative laws) to simplifycalculations where possible
Working with positive exponents and roots
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Unit 1 Working with numbers
Unit 1
Working with numbers.
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Unit 1 Working with numbers
In this unit you will learn:
How to work with the power of numbers.
How to work with scientific notation.
How we would use the power of numbers and scientific notation in our
everyday lives.
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Unit 1 Working with numbers
Table of content:
A) Power of numbers.
Definition
Rules
Using a calculator
B) Scientific notation.
Definitions
Using a calculator
C) Questions and answers.
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Unit 1 Working with numbers
A) The Power of numbers:
Definition:
It is a quick way of showing repeated multiplication.
Example:
2 x 2 x 2 x 2 x 2 x 2 = 62
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Unit 1 Working with numbers
Rules:
When you:
1. multiply powers with the same base add exponents.
e.g. x = = = 2048
Using a calculator:
key in: 2 6+5 = 2048
62
52
112
6 52
62
x
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Unit 1 Working with numbers
Rules:
When you:
2. divide powers with the same base subtract exponents.
e.g. = = = 2
Using a calculator:
key in: 2 6 - 5 = 2
62
52
62
x
6 52
12
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Unit 1 Working with numbers
Rules:
When you:
3. Raise a power to a power multiply exponents.
e.g. = = = 1 073 741 824
Using a calculator:
key in: 2 6 x 5 = 1 073 741 824
62
x
6 52
x 302
6 5(2 )
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Unit 1 Working with numbers
Questions:
Use a calculator to determine:
a) x b)
c) x d)
4242 105 85
27 3
72 2(3 )
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Unit 1 Working with numbers
Answers:
Use a calculator to determine:
a) Key in 2 4 + 4 = 256
b) Key in 5 10 8 = 25
c) Key in 7 -2 + 3 = 7
d) Key in 3 2 x 2 = 81
x
x
x
x
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Unit 1 Working with numbers
B) Scientific Notation:
Very small and very large numbers can be written in scientific notation.
It consists of a number greater or equal to 1 and less than 10, multipliedby a power of 10.
A positive power of ten e.g. gives a number greater or equal to 10and a negative power of 10 e.g. gives a number smaller than
1.
310
210
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Unit 1 Working with numbers
Examples:
a) 702 000 000 = 7,02 x
Method:
If the number is greater than 10, start at the last zero on the right handside and count the number of moves until you have a number on theleft hand side of the comma that is between 1 and 10.
b) 0,000762 = 7,62 x
Method:If the number is smaller than 1, start at the zero after the comma andcount the number of moves to the right until you have a number to theleft of the comma that is between 1 and 10.
810
410
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Unit 1 Working with numbers
Questions:
a) A human brain has about cells. This as an ordinary number is10,000,000,000
True or False?
1010
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Unit 1 Working with numbers
Questions
b) There are 105000000000000 bacteria in a culture. This
number in scientific notation is . 1,05 x
True or False?
1410
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Unit 1 Working with numbers
Question:
c) A certain virus has a diameter of 0,0000002mm.
This number in scientific notation is 2 X
True or false?
710
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Unit 1 Working with numbers
Answers:
a) = 100 000 000 000
(10 decimals to the right)
b) 105000000000000 = 1,05 x
(14 decimals to the left)
c) 0,0000002mm = 2,0 x mm
(7 decimals to the right)
1010
1410
710
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Unit 1 Working with numbers
In the American system:
A million = = 1 000 000
A billion = = 1 000 000 000
A trillion = = 1 000 000 000 000
6
10
910
1210
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Unit 1 Working with numbers
Just for fun..
Do you think you can spend a trillion rand?
If you spend a million rand a day, everyday. It will take you more than 3000years to spend a trillion rand.