Scientific Notation
Scientific Notation is an alternate way to express very large numbers or very small
numbers without an inordinate amount of zeros.
The number is written in two parts:


Just the digits (with the decimal point placed after the first digit), followed by
× 10 to a power that puts the decimal point where it should be (i.e. it shows how many
places to move the decimal point).
ex.
How to Do it
To figure out the power of 10, think "how many places do I move the decimal
point?"
If the number is 10 or greater, the decimal point has to move to the left, and
the power of 10 will be positive.
If the number is smaller than 1, the decimal point has to move to the right,
so the power of 10 will be negative:
Complete the following two tables.
Standard
Form
Scientific
Notation
Standard
Form
724
724
7240
72.4
72400
7.24
72400
0.724
724000
0.0724
7240000
0.00724
72400000
0.000724
Scientific Notation
Example
Express the following using scientific notation.
a) 45800000
b) 88303000
c) 0.000342
d) 0.0000020
We can also multiply and divide numbers in scientific notation.
Example
Multiply or divide. Express your final answer in scientific notation.
a) (4.5 x 104)(2.1 x 102)
c) (2.9 x 10-12) (5.8 x 10-30)
b) (9.7 x 106) (2 x 10-4)
d) (5.55 x 1019)2
Why Use It?
Because it makes it easier when you are dealing with very big or very small numbers,
which are common in Scientific and Engineering work.
Example: it is easier to write (and read) 1.3 × 10-9 than 0.0000000013
It is used a lot in Science:
Example: Suns, Moons and Planets
The Sun has a Mass of 1.988 × 1030 kg.
It would be too hard for scientists to have to write
1,988,000,000,000,000,000,000,000,000,000 kg
Question 1
Write 3.56 × 1011 as an ordinary number
A 3,560,000,000,000
B 356,000,000,000
C 35,600,000,000
D 3,560,000,000
Question 2
Write 7.085 × 10-14 as an ordinary number
A 0.000 000 000 007 085
B 0.000 000 000 000 708 5
C 0.000 000 000 000 0708 5
D 0.000 000 000 000 0070 85
Question 3
The speed of light in a vacuum is 299 792 458 m/s. What is this written in Scientific
notation?
A 0.299 792 458 × 109 m/s
B 29.979 245 8 × 107 m/s
C 2.997 924 58 × 108 m/s
D 2.997 924 58 × 109 m/s
Question 4 - Numbers ( Hard)
Photocopy paper is packaged in reams (500 sheets). The thickness of the pack is
41 mm. What is the thickness of one sheet of paper written in Scientific Notation
using meters?
A 8.2 × 10-2 m
B 8.2 × 10-3 m
C 8.2 × 10-4 m
D 8.2 × 10-5 m