Mr. Fig's Physics Notes

Math and Measurement

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Text Section 1.2 - Measurements in Experiments
The size (or magnitude) of quantities measured in physics can vary greatly from the very small to the very large.

For example, the diameter of a single hydrogen atom is very small but the mass of the Earth is very large
• Diameter of Hydrogen = 0.00000000001 m
• Mass of Earth = 5 974 200 000 000 000 000 000 000 kg
Scientific notation is used to write very large or very small numbers using a more compact notation. Numbers are written with a coefficient multiplied by a power of ten which specifies the number of places to the left or right of the decimal:
• Diameter Hydrogen = 1 x 10-10 m
• Mass of Earth = 5.9742 x 1024 kg
Your calculator may express these numbers using the letter "E" to stand in for "x10". A calculator could display the values shown above as:
• Diameter Hydrogen = 1E-10 m
• Mass of Earth = 5.9742E+24 kg
You should also use the "E" notation when entering small or large answers to calculations on the class website.
Scientific notation works very well when writing large and small numbers, but it doesn't exactly roll off the tongue when speaking the numbers aloud:
"the diameter of the hydrogen atom is one times ten to the minus ten power meters"
A metric prefix is used to represent the power of ten in a measurement. For example, the metric prefix nano (n) means " x 10-9 ". The metric prefix pico (p) means " x 10-12 ". The diameter of the hydrogen atom can be written in several ways, and all of them are correct:
•Diameter Hydrogen = 1 x 10-10 m = 0.1 nm = 100 pm
Here are the most commonly used metric prefixes
Power
Prefix
Abbreviation
Power
Prefix
Abbreviation
10-18
atto-
a
10-1
deci-
d
10-15
femto-
f
101
deka-
da
10-12
pico-
p
102
hecto-
h
10-9
nano-
n
103
kilo-
k
10-6
micro-
µ (mu)
106
mega-
M
10-3
milli-
m
109
giga-
G
10-2
centi-
c
1012
tera-
T