Download Order of Magnitude and Estimation

Order of Magnitude
The order of magnitude of a number is the power of ten closest to that number. Order of
magnitude is often used when dealing with very big or very small numbers associated with
macroscopic and microscopic quantities. Some are listed below.
Mass of the Universe
Mass of the Sun
Mass of the Earth
Age of the Universe
Period of visible light
Passage of light across the Nucleus
Mass of a Proton/Neutron
Mass of a Car
1050 kg
1030 kg
1025 g
1018 s
10-15 s
10-23 s
10-27 kg
103 kg
Height of a Person
Extent of the Visible Universe
Wavelength of Visible Light
Diameter of an Atom
Diameter of a Proton
Typical human Lifespan
Mass of an Electron
One Light Year (nearest star)
100 m
1026 m
10-6 m
10-10 m
10-15 m
109 s
10-30 kg
1016 m
1. Give an estimate of the order of magnitude of the following
a) The length of your arm in mm.
b) The quantity of milk you drink in a year in cm 3.
c) The mass of your backpack that contains your school materials in g.
d) The diameter of a human hair in mm.
e) The time you spend in school in a year in minutes.
f) The number of people in the country where you live.
2. Give an order-of-magnitude estimate for the time taken by light to travel across the diameter of
the Milky Way galaxy. (Diameter of Milky Way is about 1021 m)
Estimates
It is important to get a feel for reasonable estimates of everyday quantities. This often involves
estimating the results of calculations.
3. Without using a calculator estimate the value of the following expressions and then compare
with the exact value using a calculator.
a) 243 / 43
b) 2.80 x 1.90
c) 312 x 480
160
d) 8.99 x 109 x 7 x 10-6 x 7 x 10-6
(8 x 102)2
4. A rough estimate for the volume of your body in cm 3 would be closest to
A)
2 x 103
B) 2 x 105
C) 5 x 103
D) 5 x 105
5. Estimate
a)
b)
c)
d)
The dimensions of a brick
mass of an apple in grams
The period (time for one event) of a heartbeat in seconds
The temperature of a room in 0C
6. The universe is considered to have begun with the “Big Bang” event. The galaxies that have
moved the furthest are those with the greatest initial speeds. It is believed that these speeds
have been constant in time. If a galaxy 3 x 1021 km away is receding from us at 1.5 x 1011 km
y-1, calculate the age of the universe in years.
SI System of Fundamental and Derived Units
7. Which of the following is a fundamental unit in the International System of units (S.I.)?
A)
newton
B)
ampere
C)
joule
D)
pascal
8. Which one of the following lists a fundamental unit and a derived unit?
A.
ampere
second
B.
coulomb
kilogram
C.
coulomb
newton
D.
metre
kilogram
9. The resistive force F acting on a sphere of radius r moving at speed v through a liquid is
given by
F = cvr
where c is a constant. Which of the following is a correct unit for c?
A.
N
B.
Ns
–1
C.
2 –1
Nm s
D.
Nm
–2
s