Standard form is a way of writing down very large or very small numbers
easily. 10³ = 1000, so 4 × 10³ = 4000 . So 4000 can be written as 4 × 10³ . This
idea can be used to write even larger numbers down easily in standard
form. Small numbers can also be written in standard form. However, instead of
the index being positive (in the above example, the
index was 3), it will be negative.
The rules when writing a number in
standard form is that first you write down a number between 1 and 10, then you
write × 10(to the power of a number).
Example
Write 81 900 000 000 000 in standard form:
81 900 000 000 000 = 8.19 × 10^{13}
It’s 10^{13} because the decimal point has been
moved 13 places to the left to get the number to be 8.19
Example
Write 0.000 001 2 in standard form:
0.000 001 2 = 1.2 ×
10^{6}
It’s 10^{6} because the decimal point has been
moved 6 places to the right to get the number to be 1.2
On a calculator, you usually enter a number in standard form
as follows: Type in the first number (the one between 1 and 10). Press EXP .
Type in the power to which the 10 is risen.
Manipulation in Standard Form
This is best explained with an example:
Example
The number p written in standard form is 8 ×
10^{5}The number q written in standard form is 5 ×
10^{2} Calculate p × q. Give your
answer in standard form.
Multiply the two first bits
of the numbers together and the two second bits together: 8 × 5 ×
10^{5} × 10^{2}
= 40 × 10^{3}
(Remember 10^{5} × 10^{2} =
10^{3})
The question asks for the answer in
standard form, but this is not standard form because the first part (the 40)
should be a number between 1 and 10.
= 4 ×
10^{4}
Calculate p ÷ q. Give your answer in
standard form.
This time, divide the two
first bits of the standard forms. Divide the two second
bits.
(8 ÷ 5) × (10^{5} ÷
10^{2})
= 1.6 ×
10^{7}
Copyright © Matthew Pinkney 2003
