Index/Power
The small, raised number next to a normal letter or number, to be multiplied by itself
Example
b2= b x b
43 = 4 x 4 x 4
Square power 2 : 2
- multiplying by itself
Example
(1) Square of 4 = 42 = 4 x 4 = 16
(2) 32 = 3 x 3 = 9
(3) Square of (-5)2 = (-5) x (-5) = 25
Perfect Square are the squares of whole numbers:
(2 x 2) 4, (3 x 3) 9, (4 x 4) 16, …
Square Root - the Opposite of Square
A number that when multiplied by itself, gives the number
Symbol: √
5 --> square 52 --> 25
5 <-- Square root √25 <-- 25
Example
(1) 16 = 4 x 4
√16 = 4
(2) a2 = 25
a = + √5 x 5 = = +5
Why +5 when a number is square-root?
(-5) x (-5) = 25 ( -ve x -ve = + ve)
5 x 5 = 25
=> 25 = (-5)2 = 52 = 25
a2 = + √a x a = -a or a
Cube - Power of 3 : 3
- Multiplying the number by 3 times
Example:
(1) Cube of 3 = 33 = 3 x 3 x 3 = 27
(2) 43 = 4 x 4 x 4 = 64
(3) cube of (-5) 3 = (-5) x (-5) x (-5) = = -125
Cube Root
A value that when ‘cubed’ gives the original number
Symbol: 3√
4 --> cube 43 --> 64
4 <-- cube root 3√64 <-- 64
Example:
3√8 = 3√2 x 2 x 2 = 2
3√216 = 3√6 x 6 x 6 = 6
Index Notation
- Representing number/letters that multiplied themselves a number of time
Example
Write 18 in index notation
Using LCM :
2 | 18 (smallest divisible no=2, 18/2=9 , place 9 below)
3 | 9 (next smallest no to divide:3)
3 | 3 (divide by 3, till = 1)
1
The index notation of 18 = 2 x 3 x 3
= 2 x 32
Example
Write 40 in index notation
Using LCM :
2 | 40 (smallest divisible no=2, 40/2=20 , place 20 below)
2 | 20 (next smallest no to divide:2)
2 | 10 (next smallest = 2)
5 | 5 (next smallest = 5, till = 1)
1
The index notation of 40 = 2 x 2 x 2 x 5
= 23 x 5
STANDARD FORM (S3/NA/T)
K x 10m where K is between 1 to 9 1 <= K < 10
Example:
Change 123.5 to standard form
Step 1: Change number to 1 <= k < 10
123.5 = 1.235 x 100
Step 2: Change to 10n
100 = 102
Step 3: Answer in standard form
123.5 = 1.235 x 102
Example: Change 0.0012 to standard form
0.0012 = 1.2 x 0.001 (Step 1: Change number to 1 <= k < 10)
0.001 = 10-3 (Step 2: Change to 10n )
0.0012 = 1.2 x 10-3 (Step 3: Answer in standard form)
Practice
1. Calculate (6.2 x 103) x (1.5 x 106). Give your answer in standard form.
2. Find the value of
(a) 83
(b) 5-2
3. Write 0.0000567 in standard form.
4. Calculate 6.1 x 106 + 1.4 x 107. Give your answer in standard form.
5. Find the value of 24 + 52
6. Write the number 315.17
(a) in standard form
(b) correct to one decimal place
(c) correct to the nearest 10.
7. Write 4.67 x 106 as an ordinary number
8. Calculate (6.2 x 103) x (1.5 x 106). Give your answer in standard form.
9. Write the number 3.6148 correct to
a. 4 significant figures
b. 2 decimal places
