Index Notation Worksheet Page 2
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1
2NUMBER AND ALGEBRA
• NUMBER AND PLACE VALUE
Write the following using index notation.
4
2 ì 2 ì 3
3 ì 3 ì 3 ì 3 ì 2 ì 2
a
b
5 ì 5 ì 2 ì 2 ì 2 ì 2
7 ì 2 ì 2 ì 2
c
d
5 ì 11 ì 11 ì 3 ì 3 ì 3
13 ì 5 ì 5 ì 5 ì 7 ì 7
e
f
2 ì 2 ì 2 ì 3 ì 3 ì 5
3 ì 3 ì 2 ì 2 ì 5 ì 5 ì 5
g
h
5
Write 6
using a repeated multiplication (that is, in expanded form).
5
Write each of the following using repeated multiplication (that is, in expanded form).
6
3
9
6
11
4
5
a
b
c
Write the following numbers in expanded form using index notation.
7
WE2
a
300
b
4500
c
6785
10 000
31 702
200 301
d
e
f
Simplify each of the following by fi rst writing as a repeated multiplication and then
8
WE3
using index notation.
ì 5
ì 7
ì 4
8
3
2
6
8
5
5
7
4
a
b
c
7
3
3
8
5
3
(2
)
(11
)
(9
)
d
e
f
(3 ì 13)
6
(2 ì 5)
4
(5 ì 7)
5
g
h
i
UNDERSTANDING
Which of the following expressions has the greatest value?
9 a
MC
8
2
4
3
2
2
8
3
4
9
A
B
C
D
E
Justify your answer using mathematical reasoning.
b
4
The value of 4
is:
10
MC
8
16
64
256
484
A
B
C
D
E
3
ì 3
2
Find the value of 2
.
11
Evaluate each of the following.
12
ì 4
+ 9
ó 2
4
3
5
3
3
5
3
3
8
a
b
c
4
- 9
3
3
+ 2
5
ì 9
2
7
- 4
5
ó 2
6
d
6
e
5
f
2
REASONING
2
= 144 and 21
2
= 441. It is also true that 13
2
= 169 and 31
2
= 961.
We know that 12
13
2
= 196 will 41
2
= 691? Try to justify your answer without calculating 41
2
If 14
.
There is a shortcut that allows you to square any
14
number that ends in 5. Look at the following examples
REFLECTION
and see if you can identify the rule. Use your rule to
2
2
evaluate 75
and 95
.
Why do we use index notation?
= 225, 25
= 625, 35
= 1225, 45
= 2025
2
2
2
2
15
Prime numbers and composite
3B
numbers
Prime numbers
A
prime number
is a counting number that has exactly 2 factors, itself and 1.
I
(Counting numbers are 1, 2, 3, 4, . . . .)
The number 3 is a prime number. Its only factors are 3 and 1.
I
The number 2 is the only even prime number. Its only factors are 2 and 1.
I
composite number
A
is one which has more than two factors.
I
The number 4 is composite. Its factors are 1, 2 and 4.
I
The number 1 is a special number. It is neither a prime number nor a composite number
I
because it has only one factor, 1.
71
Chapter 3
Indices and primes
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