Metric Conversions/Scientific Notation/
Dimensional Analysis
Adv Physics
Chapter 1 Review
Measuring Systems
 Two major systems of units in use today
- metric system
- British system (only used by US)
International System of Units
 Abbreviated SI
 Modern version of the metric system
 Designates base units
Length
 Meter (m)
 Originally defined as 1/10000000 of the distance
from the North Pole to the equator along a
meridian running through Paris
 Today 1 m is the distance traveled by light in a
vacuum in 1/299792458 seconds
Mass
 Kilogram (kg)
 Referenced to a standard kept at the International
Bureau of Weights and Measures in France
Time
 Second (s)
 Defined by the radiation frequency of the cesium
– 133 atom
 1 second = 9192631770 oscillations
Metric System
 Major advantage is that it is based on powers of
10
 Most common prefixes are kilo-, centi-, and
milli-
Dimensional Analysis
 Method of using equivalence statements to convert
from one unit to another
 Example –
Convert 12 feet into yards.
12 ft x (yd / 3 ft) = 4 yd
Dimensional Analysis
This is the Method I want you to use:
 Place the unit you want as your answer on top.

Place the unit you want to cancel on the bottom.
 Always go to the base 1st!!!!
 Notes: Always place the power of 10 with the base unit
(example: 10^3 m) --- base units will be m, g, s, etc.
 Does the answer make sense?
STAIR STEP
 If between k(kilo) and m(milli) you can use stair step
method… (ex: 20km to 1 dm)
 kentucky
10^3
20.0
has
10^2
dark
10^1
black
base
deep
10^-1
coal mines
10^-2 10^-3
Answer
Dimensional Analysis
1.
Convert 20 km to m.
2.
Convert 100g to dg .
Dimensional Analysis
1.
Convert 5 μm to m.
2.
Convert 500 kg to Mg .
3.
Convert 4500 ps to ns.
4.
The area of an object is 137 km2. Express this
area in m2.
Scientific Notation
 Easier method of writing really small or really large
numbers
 Ex – 3,400,000 is the same as 3.4 x 106
 Ex – 0.00047 is the same as 4.7 x 10-4
Scientific Notation
1.
Express 53,200,000 in scientific notation.
2.
Express 0.0004 in scientific notation.
3.
Express 57.52 in scientific notation.
4.
Express 0.00000056 in scientific notation.
Dimensional Analysis #2
 Convert 12 years to minutes.
 Convert 23 miles to km (1 mile = 5280 ft, 3.28 ft = 1 m).
 Convert 5 mph to m/s.
 How many seconds would it take to run a mile(1.6 km) at
the 5 mph? (how many minutes is this?)