Download Standard Form

Interactive Maths Worksheets
Developing & Refreshing Your Maths Skills
Standard Form
Index Notation
To understand standard form it is, first of all, essential to
understand the index notation.
32 = 3 x 3
33 = 3 x 3 x 3
So using index notation is a shorthand way of writing large numbers
and allows for easier calculations.
If a number has a negative index it will calculate as a number less
than 1:
e.g. 3-2 is the same as 1
32
e.g. 10-1 is the same as 1
101
0.1 = 1 = 10-1
10
0.01 =
1 = 10-2
100
0.001 =
1 = 10-3
1000
This table shows how large and small numbers can be represented
by using powers of 10.
0.0001 0.001 0.01 0.1
10-4
10-3
1
10 100 1000 10,000 100,000
10-2 10-1 100 101 102
103
104
105
Interactive Maths Worksheets
Developing & Refreshing Your Maths Skills
Standard Form
Standard Form (Scientific Notation)
Standard form is a way of expressing large numbers in a more
manageable format. It is very lengthy to keep writing large figures
and there is more margin of error as there is always the risk of
leaving out or adding 0's.
0.0000003067 is easy to misread. Mistakes in a 0 here or there
will make a serious difference. 3.067 is much easier to read but
isn't correct.
Standard form gives a way to write very big and very small
numbers without getting lost in a whole string of 0's.
Numbers in Standard Form
A number conforms to Standard Form Index when it is written as:
a x 10n
Where 'a' only has a single digit between 1 and 9 before the decimal
place and 'n' is an integer (a positive or negative whole number, or
0)
These two numbers multiplied together equal the value of the
intended number.
So:
1200 can be written as 1.2 x 103 (1.2 x 1000)
790 can be written as 7.9 x 102 (7.9 x 100)
0.0371 can be written as 3.71 x 10-2 (3.71 ÷ 100)
Interactive Maths Worksheets
Developing & Refreshing Your Maths Skills
Standard Form
How to Write Numbers in Standard Form
To convert numbers into standard form you consider how to
represent your number in the form of a x 10n
1. How could the number written so that only one digit (not a
zero) is in front of the decimal place?
e.g. 850 --> 8.5
2. Then think what you did to that number to get there.
e.g. 850 is 8.5 x 100 (8.5 x 102)
To convert numbers from their standard form you are multiplying
or dividing by powers of 10.
If the index is a positive number then you are multiplying (i.e.
moving the decimal place to the right ) to return the number to its
equivalent bigger form.
If the index is a negative number then you are 'dividing' ( i.e.
moving the decimal place to the left ) to return the number to its
equivalent smaller form.
Do quiz 1
Interactive Maths Worksheets
Developing & Refreshing Your Maths Skills
Standard Form
Calculating with Numbers in Standard Form
You can calculate very large numbers in their non-standard form
but be careful as there are opportunities for mistakes to be made
given the amount of figures to be kept in their proper places (to
represent their correct place value).
To multiply (x) numbers in Standard Form, multiply the numbers
and ADD the integers.
e.g. (4.5 x 105) x (2.1 x 102)
= (4.5 x 2.1) x (105 x 102)
= 9.45 x 10(5+2)
= 9.45 x 107
To divide (÷) numbers in Standard Form, divide the numbers and
SUBTRACT the integers.
e.g. (1.874 x 106) ÷ (1.8 x 103)
= (1.874 ÷ 1.8) x (106 ÷ 103)
= 1.04 x 10(6-3)
= 1.04 x 103
To add (+) or subtract (-) numbers in Standard Form, first
change them into non-standard form and make sure they maintain
their correct place value. Then do the calculation and convert back
into Standard Form.
Or Convert the numbers to the same power (order of magnitude)
and then + or - the coefficients.
e.g. (3.7 x 10-10) + (8.9 x 10-11)
= (3.7 x 10-10) + (0.89 x 10-10)
= 4.59 x 10-10
Do quiz 2