Measurements
What do we measure?
 Fundamental properties
 mass (weight)
 length
 time
 temperature

kilogram
meter
second
Kelvin
Derived quantities
 density, velocity, force, etc...
Using the metric system
 In the metric system, prefixes are used
to identify the multiples of ten.
 103
102 101
1
10-1 10-2 10-3
 Kilo Hecto Deka BASE Deci Centi Milli
Base units
 mass
gram(g)
 length
meter (m)
 liquid volume
liter (l)
 time
second (s)
Each multiple is one decimal place.
Move the decimal to convert
Moving the decimal

For measurements that are defined by a
single unit such as length, mass, or liquid
volume , etc., simply move the decimal the
number of places indicated by the prefix.
 400


m =
40,000 cm
75 mg = 0.075 g
For area measurements, they are the
combination of two dimensions, you move
the decimal twice the number of places.
 2.5
m2 = 2,500,000 mm2
Converting measurements
 Metric
Metric
 multiples of 10
 move decimal or use conversions
 English
 conversion
Metric
factors
 unit cancellation method
Converting Metric English
When converting in the US (English) system or
converting between US and metric units it is
necessary to use proportions.
 In the example below, the measurement 12 in.
is converted to cm. The conversion factor 1 in
= 2.54cm is written as a ratio.

 12 in. x 2.54 cm
1 in.
= 30.48 cm
Practice
A rattlesnake is 2.44 m long. How
long is the snake in cm?
1) 2440 cm
2) 244 cm
3) 24.4 cm
Solution
A rattlesnake is 2.44 m long. How long is the
snake in cm?
2) 244 cm
2.44 m x 100 cm
1m
= 244 cm
What is wrong with the following setup?
1.4 day
x 1 day
24 hr
x
60 min
1 hr
x 60 sec
1 min
1.4 day
x 1 day
24 hr
Units = day2/hr2
x
60 min
1 hr
x 60 sec
1 min
Not the final unit needed
Steps to Problem Solving
Read problem
 Identify data
 Write down a unit plan from the
initial unit to the desired unit
 Select conversion factors
 Change initial unit to desired
unit
 Cancel units and check
 Do math on calculator
 Give an answer using
significant figures

If the ski pole is
3.0 feet in length,
how long is the
ski pole in mm?
3.0 ft x 12 in x 2.54 cm x 10 mm =
1 ft
1 in.
1 cm
Significant digits
 The digits reported in a measured
quantity
 Indicate the precision of the
measuring instrument
 Calculations should not have more
significant digits than the least
number of significant digits in the
problem.
Rules – Significant Digits
 1.
All nonzero numbers are
significant. Ex: 456 – 3 sig.
 2. All zeros between numbers are
significant. Ex: 408 – 3 sig.
 3. If decimal present, zero’s to the
left are not significant.
Ex: 0.0078 – 2 sig.
 4. If decimal present, zero’s to the
right are significant.
Ex: 0.090 – 2 sig.
 5. If no decimal, zero’s on end are
not significant. Ex: 34500 – 3 sig.
Adding and Subtracting
 In addition and subtraction, round up
your answer to the least precise
measurement or least number of
places behind the decimal.
 For example:
24.686 + 2.343 + 3.21 = 30.239 =
30.24
 3.21 is the least precise
measurement.
Multiplying and Dividing
 In multiplication and division,
round it up to the least number
of significant digits.
 For example:
3.22 * 2.1 = 6.762 = 6.8
 2.1 contains 2 significant digits.
Scientific Notation
 Used for expressing very large or
very small values
 standard form

base x 10 exponent
base is between 1.0 and 9.999…
if exponent is positive the value is greater than 1

if exponent is negative the value is less than 1


 convert to decimal by moving the
decimal the number of places
indicated by the exponent