grade 10 unit 1 working with numbers

7/31/2019 Grade 10 Unit 1 Working With Numbers

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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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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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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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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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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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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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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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Questions:

Use a calculator to determine:

a) x b)

c) x d)

4242 105 85

27 3

72 2(3 )


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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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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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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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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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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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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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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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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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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.

grade 10 unit 1 working with numbers

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