Transcript The Metric System

The Metric System
Why do I need to learn and be able
to use the metric system?
Everyday Metric
• http://www.nisenet.org/viz_lab_image_scaler
Standard International Units (SI)
Base Units
Quantity
Unit
Symbol
Length
Meter
m
Mass
Kilogram
kg
Moles
mole
mol
Time
Second
s
Temperature
Kelvin
K
Metric Conversions
Prefix
giga
mega
kilo
Base Unit
deci
centi
milli
micro
nano
pico
Metric Prefix Table
Symbol
Multiplier
G
1,000,000,000
M
1,000,000
k
1,000
1
d
0.1
c
0.01
m
0.001
µ
0.000001
n
0.000000001
p
0.000000000001
Exponential
109
106
103
100
10¯1
10¯2
10¯3
10¯6
10¯9
10¯12
Nanoscience
• 1 human hair is ~50,000 nanometers across;
or 50 nanometers is one-thousandth the
width of a human hair.
• 1 bacterial cell measures a few hundred
nanometers across.
• The smallest things the naked eye can see are
10,000 nanometers.
• 1 nanometer = 10 hydrogen atoms in a line.
Why should I care about nanoparticles?
Because it is being used now!
Untrathin glass treatment
Nanocrystals are used in photovoltaic cells as well as drug research
Using nanotechnology, Cornell scientists created a
fabric that can detect biohazards like E. coli and
other pathogens.
Stain repellent clothing
sunscreen
Antibacterial paint in hospitals
Other Prefixes
How to Convert
• Memorize the conversion factors.
• When moving from a large prefix to a smaller
prefix your answer will always be a larger
number. EX: 1 megameter = 107 decimeter
• When converting a small prefix to a larger
prefix your answer will always be a smaller
number. EX: 1 nanometer = 10-7 centimeter
Dimensional Analysis
Follow these steps to set up a dimensional analysis problem
1.
2.
3.
4.
5.
List all given information with the correct units.
Write down what you are trying to determine along with the correct unit.
List the conversion factors needed to solve the problem.
Write your given information as a fraction with the correct units.
Set up a chain of “fractions” (conversion factors) to convert from the given
units to the desired units. To cancel out the original unit, place that same
unit in the denominator where it will cancel out later.
6. Verify that all units cancel out except the units of the desired answer.
7. Do the math and record the final answer to the correct number of
significant digits and in proper scientific notation. Include the correct
units.
8. Circle your final answer.
Dimensional Analysis Problem
• What is the size in cm of a 15 nm gold particle?
1. 15 nm
2. ?cm
3. 1m = 109 nm and 1m = 100 cm
4. 15 nm
1
5. 15 nm l 1m
l 100cm = 15 x 10-7 cm
1 l 109 nm l 1m
= 1.5 x 10-6 cm
CNN News Headline
NASA: Human error caused loss of Mars orbiter
November 10, 1999
WASHINGTON (AP) -- Failure to convert English measures to metric values
caused the loss of the Mars Climate Orbiter, a spacecraft that smashed into
the planet instead of reaching a safe orbit, a NASA investigation concluded
Wednesday.
The Mars Climate Orbiter, a key craft in the space agency's exploration of the
red planet, vanished after a rocket firing September 23 that was supposed to
put the spacecraft on orbit around Mars.
How To Measure
• Lab equipment is calibrated to a certain
accuracy that is unique to each piece of
equipment, so your recorded measurement
can not always contain 1 or 2 decimal places.
• You determine how to record your
measurement based on the calibration of the
tool.
First Let’s Define
• Accuracy: How close a measurement is to the
true value. Your measurement tool has an
effect on the accuracy of a measurement
• Precision: How repeatable are your
measurements. This is more reflective of your
lab technique.
So How Do We Measure With Accuracy?
• Look at the calibration lines on your tool.
• You know the measurement at these lines, but
you do not know how far it is between the
lines.
• You record what you know and guess between
the lines.
• The last digit given for any measurement is
the uncertain or estimated digit
• Lets take a look
Read the Bottom of the Meniscus
Which is correct? 66 ml, 66.0 ml, 66.1 ml, 67 ml, 67.0 ml, 67.5 ml
Practice
• 1cc = 1 cubic
centimeter= 1 ml
• Calibration lines every
0.5 cc
• Guess between the
lines
• Which is correct? 8 cc,
8.0 cc, 8.5 cc
Another Example
• How is this tool
calibrated?
• What is the correct
volume? 80 ml, 85 ml,
87ml, 90 ml
And There’s More
Last One
Significant Digits
• AKA significant figures or sig digs or sig figs
• Determined by the measuring tool so they
relate the accuracy of the tool.
• Used to determine the number of significant
digits in a calculated answer.
• You can not calculate an answer that is more
accurate than the least accurate
measurement.
Rules to Determine # Sig Digs
There are three rules on determining how many
significant figures are in a number:
• Non-zero digits are always significant.
• Any zeros between two significant digits are
significant.
• A final zero or trailing zeros in the decimal
portion ONLY are significant.
Practice
Identify the number of significant figures:
1) 3.0800
2) 0.00418
3) 7.09 x 10¯5
4) 91,600
5) 0.003005
6) 3.200 x 109
7) 250
8) 780,000,000
9) 0.0101
10) 0.00800
Calculations With Sig Digs
RULE: When multiplying or dividing, your answer may only show as
many significant digits as the multiplied or divided measurement
with the least number of significant digits.
Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm =
5946.50525 cm3
• Check the number of significant digits in each of the original
measurements:
22.37 shows 4 significant digits.
3.10 shows 3 significant digits.
85.75 shows 4 significant digits.
• Our answer can only show 3 significant digits because that is the
least number of significant digits in the original data.
• 5946.50525 shows 9 significant digits. We must round in order to
show only 3 significant digits. Our final answer becomes 5950 cm3.
Calculations With Sig Digs
RULE: When adding or subtracting your answer can only
show as many decimal places as the measurement having
the fewest number of decimal places.
Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g
• Look to the original problem to see the number of decimal
places shown in each of the original measurements.
3.76 shows 2 decimal places
14.83 shows 2 decimal places
2.1 shows 1 decimal place
• We must round our answer to one decimal place (the tenth
place). Our final answer is 20.7 g
Practice Problems
Solve the following problems and report answers with
appropriate number of significant digits.
1) 6.201 cm + 7.4 cm + 0.68 cm + 12.0 cm = ?
2) 1.6 km + 1.62 m + 1200 cm = ?
3) 8.264 g - 7.8 g = ?
4) 10.4168 m - 6.0 m = ?
5) 12.00 m + 15.001 kg = ?
6) 131 cm x 2.3 cm = ?
7) 5.7621 m x 6.201 m = ?
8) 20.2 cm divided by 7.41 s = ?
9) 40.002 g divided by 13.000005 ml = ?