Download Standard (Index) Form

Standard (Index) Form
Standard (Index) Form is a simple way to write very large and very small numbers.
The ‘Standard’ refers to the fact that all numbers have a similar appearance when
written in ‘standard form’. The ‘Index’ refers to the index or power.
All numbers in Standard Form take this form:
a x 10x
where 1  a  10
and x is an integer (positive or negative whole number)
(but 1000000 = 106)
4000000 = 4 x 1000000
= 4 x 106
56000 = 5.6 x 10000
= 5.6x 104
(don’t forget ‘number’ must be between 1 and 10)
Also works for very small numbers.
If we want to write a small number in Standard Form the ‘power’ will be negative.
0.0002 =
2
= 2 = 2 x 10-4
10000
104
0.000092 =
9.2
=
100000
9.2
105
(see notes on powers)
= 9.2 x 10-5
On a calculator, we can enter numbers in Standard Form by using the EXP or EE
button. If you are not sure which button it is on your calculator then ask your maths
teacher.
To enter 3.2 x 107 on a calculator press:
EXP
3
.
2
or
7
EE
The biggest problem with calculators is that different calculators display numbers
written in Standard Form in different ways.
If your calculator display shows 2.31 04 , or 2.31 04 or 2.31 E 04 this
means 2.31
x 104
- if you are not sure then ask your maths teacher.
Multiplying with Standard Form is easy because it does not matter which order you
multiply in (multiplication is commutative)
3 x 108 x 2 x 105 = 3 x 2 x 108 x 105
= 6 x 1013
4 x 105 x 7 x 1011 = 4 x 7 x 105 x 1011
= 28 x 1016
= 2.8 x 10 x 1016
= 2.8 x 1017
Watch out for ‘negative powers’.
(This is not in Standard Form yet)
4 x 105 x 7 x 10-11 = 4 x 7 x 105 x 10-11
= 28 x 10-6
= 2.8 x 10 x 10-6
= 2.8 x 10-5
Dividing with numbers written in Standard Form needs to be slightly more ordered.
6 1011
6 1011
6 x 10 ÷ (3 x 10 ) =
=  4 = 2 x 107
3 10
3 104
11
4
3 x 1014 ÷ 6 x 105 =
3 1014
(not in Standard Form)
 5 = 0.5 x 109
6 10
= 5 x 10-1 x 109
= 5 x 108
When it comes to adding and subtracting with numbers in standard form, we need to
write them out in full first.
3 x 104 + 6.2 x 105 = 30000 + 620000 = 650000 = 6.5 x 105
7.2 x 105 – 2.3 x 104 = 720000 – 23000 = 597000 = 5.97 x 105
Past Paper Question
5 x 104 x 8 x 106 = 5 x 8 x 104 x 106
= 40 x 1010
(not in Standard Form)
10
= 4 x 10 x 10
= 4 x 1011
2 104 2 104
 
 0.25 102 = 2.5 x 10-1 x 10-2
8 106 8 106
= 2.5 x 10-3
(not in Standard Form)