Standard Form
A number expressed in standard form is a number written between 1
and 10 multiplied by 10 to an appropriate power.
The use of standard form is to represent very small numbers or very
large numbers
For example
0.000 000 000 000 32 represented in standard form will be
214000 000 000 represented in standard form will be
3 . 2  10
2 . 14  10
11
 13
Example
Express each of the following in standard form
(i) 0.000 000 462
(ii) 0.004
(iii) 90 000
(iv) 5910 000 000
Example
Express each of the following as ordinary numbers
(i)
1 . 6  10
8
(ii) 2 . 54  10  6
(iii)
7  10
12
(iv) 9 . 414  10  2
Example
Write the following list in order of size starting with the smallest
1 . 5  10
8
8 . 7  10
1
, 27 000 000, 3 . 7  10
4
, 0.000 44, 3 . 2  10
7
Example
The surface of the earth is about 509 970 000 km2. Express this
in standard form correct to two significant figures.
Example
Without a calculator work out the following and give your answer in
standard form.
(a)
30 x 40 000
(b)
12 000 x 0.00005
(c)
1 . 1  10   6  10 
(d)
5 . 4  10   9  10 
(e)
0 . 00072  80000000
5
6
3
7
Example
Work out the following
(a) 360000  24000000
(b) 0 . 0004  20 000 000
Example
4
7
Given that A  6  10 and B  4  10 work out, without a
calculator
(i) AB
(ii)
A
B
Example
5
Given that X  1 . 2  10
and Y  5  10
9
work out , in standard form
(i)
(ii)
XY
X
Y
Here we use the button
1
.
2
–
EXP
And for Y we type
5
EXP
for the standard form and type for X
5
EXP
–
9
Example
A rectangle has length AB = 1 . 3  10 km and width BC = 2 . 5  10 km.
5
Giving your answer in standard form, find
a) the area,
b) the perimeter of this rectangle.
4