GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
Real numbers, irrational numbers, scientific notation
SECTION A: TYPICAL EXAM QUESTIONS
Question 1: 10 minutes (Taken from Examination Aid)
(Always see how many numbers are recurring and the equation is multiplied by a
multiple of 10)
Convert the following decimals into common fractions :
1.1
0, 3
*( if 1 number is recurring, the equation is multiplied by 10)
1.2
0,1 2
1.3
0,1 2 3 *( if 3 numbers are recurring, the equation is multiplied by 1000)
 
*( if 2 numbers are recurring, the equation is multiplied by 100)
  
Question 2: 25 minutes (Taken from Examination Aid)
( remember the square brackets and closed dot is included, round brackets and open dot not
included when working with number lines and interval notation)
2.1. Represent on a number line and write in interval notation :-
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GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
2.2.
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GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
SECTION B: SOLUTIONS AND HINTS
Question 1 :

1.1
0, 3
letx  0,333333...............1
10 x  3,333333................2
2 1
9x 3

9 9
1
x
3
  
0,1 2 3
letx  0,123123123...................1
1.3
1000x  123,123123...................2
2 1
999 x 123

999 999
41
x
333
Question 2:
(Interval notation does not apply to natural , whole or integers, only real numbers)
2.1.
The last one is the only one with interval notation :
2.2.
*
*
*
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GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
SECTION C: ADDITIONAL CONTENT NOTES
NUMBERS – the symbols are important because these numbers get referred to by their
symbols. You must know these definitions
 = natural numbers = { 1;2;3;4…} - these are counting numbers starting from 1
 0 = whole numbers = { 0;1;2;3;…} – these are counting numbers starting from zero
 = integers = { -2;-1;0;1;2;…} – these are positive and negative whole numbers
Q = rational = {+ve and –ve recurring fractions } – these are numbers that can be
expressed in the form of a fraction and the numbers used are integers.
Q  = irrational = { non-recurring decimals } – these are numbers that ‘never end’ – in other
words they have no pattern after the decimal.
R = real = { almost everything }
- any number that exists

All integers are rational numbers.
Eg. the number 5 can be written as where 5 and 1 are integers.

Mixed fractions are rational numbers
Eg.
where 11 and 4 are integers.

Terminating decimals are rational numbers.
Eg.
where 3 and 4 are integers.
IRRATIONAL NUMBERS
When looking for irrational numbers, find an integer smaller than that number that can be
square rooted easily and an integer that is larger than that number that can also be square
rooted easily. That irrational number lies between those integers on a number line.
WORKED EXAMPLE
-
- the integer before is 5 (
the integer after is 6 (
This irrational number lies between 5 and 6
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GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
SECTION D: HOMEWORK
1. Write
as a decimal fraction.
(1)
2. A set of numbers is represented on the number line below :
-3
4
2.1.1. Use inequalities to describe the set of numbers.
2.1.2. What is the smallest integer in this set of numbers ?
(2)
(1)
3. State whether the following statements are true or false. If false, explain your answer.
3.1 The first prime number is one.
3.2 The set of whole numbers is closed under the operations of addition and
subtraction.
3.3 When an integer is divided by another integer, the answer is not always an integer.
3.4 Recurring decimals do not terminate and therefore cannot be written as fractions.
3.5 The distributive law states that a( b + c ) = ab + ac
(7)
(Taken from Examination Aid)
4. Convert
to a common fraction in its simplest form.
(4)
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GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
SECTION E: SOLUTIONS TO SESSION 7
2.3
1.1
1.2.
2.1
2.2
68,660
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GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME
Mathematics
Grade 10
Session 8
(LEARNER SET)
QUESTION 3
The angle formed is 70,5
(6)
C
QUESTION 4
.
10
.
B
8,34
A
QUESTION 5
The SSIP is supported by
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