Transcript Measurements Powerpoint

Measurements
What do we measure?


Fundamental properties
 mass (weight) kilogram
 length
meter
 time
second
 temperature
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
Metric
conversion 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 = 30.48 cm
1 in.
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