scientific measurement and conversions / dimensional analysis
DESCRIPTION
Scientific Measurement and Conversions / Dimensional Analysis. Using and Expressing Measurements. Measurement A quantity that has both a NUMBER and a UNIT From now on: u nits are metric* Scientific Notation Product of a coefficient and 10 raised to a power Coefficient must be 1 ≤ # ≥ 9 - PowerPoint PPT PresentationTRANSCRIPT
Scientific Measurement and Conversions /
Dimensional Analysis
Using and Expressing Measurements
Measurement A quantity that has both a NUMBER and a UNIT
From now on: units are metric*
Scientific Notation Product of a coefficient and 10 raised to a power
Coefficient must be 1 ≤ # ≥ 9 100 = 1 101 = 10 Use “EE” or “EXP” or “E” button
means “times 10 to the”
Accuracy, Precision, and …
Accuracy How close a measurement comes to the actual or true
value of whatever is measured How close to the bulls-eye did your dart(s) land?
Precision How close a series of measurements are to one
another How close together are all your darts? (regardless of
proximity to bulls-eye)
What darts?
And …. Error
Error = experimental value – accepted value Exp value = measured in lab Accepted value = correct value based on references or
math (formulas)% error = l error l x 100 %
accepted % error = (the absolute value of experimental error –
accepted value) divided by the accepted value, times 100 to make it a %
Significant Figures
ALL “known” digits + 1 “estimated” digit Known are digits clearly marked by instrument
increments Estimated is the smallest increment divided by 10
So if ruler marks off millimeters (0.001 m) then the unknown digit will be the ten-thousandths’ place (0.0001 m)… or 0.1 mm
Sig figs can be annoying, but it is important to only record measurements to the most or least precise it can be…
Visual example…
Rules … you’re given a measurement, are the digits sig?
NONZERO digits are significant – always! 1998 m = 4 sig figs
EMBEDDED zeros are significant – always! 2002 L = 4 sig figs
LEADING zeros are NEVER significant 0.08 g = 1 sig fig
(because could be written as 8 X 10-2 g…clearly 1 sig fig)
Trailing zeros are NOT sig, UNLESS a decimal point is involved 2010 mg = 3 sig figs, BUT 201.0 cg = 4 sig figs; 2010. mg = 4 sig figs
although that format is frowned upon because it could and should be written as 2.010 x 103 mg (obviously 4 sig figs still)
Unlimited number of sig figs? Woohoo!
Counted numbers 24 students in the classroom 5 “digits” on my hand
Defined quantities 60 minutes = 1 hour 100 pennies = 1 dollar 100 cm = 1 m
Rounding- you’re not in math class anymore…
If digit ≤4, truncate (drop) 2.22 cm 2.2 cm
If digit > 5, round up 1.68 cm 1.7 cm
If digit = 5, look at numbers after OR before If there is a NONZERO digit AFTER a 5, round the 5 up (ex: 1.251 cm 1.3 cm) If there is a ZERO or NO DIGIT after a 5, look at the digit BEFORE
If digit is EVEN, truncate 5 (ex: 1.250 cm 1.2 cm) If digit is ODD, round up (ex: 1.15 cm 1.2 cm)
Mo Rounding!
Sig Figs in calculations = more rules
A calculated answer can NEVER be more precise than the least precise measurement from which it is calculated Think “a chain is only as strong as its weakest link”
Addition & Subtraction Keep the LEAST number of DECIMAL PLACES
1.8 mL + 2 mL = 3.8 mL 4 mL (must round to “ones”)
Multiplication & Division Keep the LEAST number of SIGNIFICANT FIGURES
1.8 m X 2.71 m = 4.878 m2 4.9 m2 (must round to 2 figures) Yes, PEMDAS is still in effect
Addition & Subtraction practice
Mult & Div practice
QUESTIONS??
Dimensional Analysis
Dimensional Analysis uses MULTIPLICATION and SIMPLE CONVERSION FACTORS to move from one unit to another.
Convert 2 feet to inchesWe need a conversion factor, a relationship
between the units
Dimensional Analysis
These both give us a relationship between in. and ft.
We use D.A. to cancel units
Dimensional Analysis
The units cancel out leaving only
Giving us an answer of 24 in.
Dimensional Analysis
Convert 48 inches to feet.
Dimensional Analysis
Convert 5 days to hours.
Dimensional Analysis
How many seconds are there in 4 minutes?
Dimensional Analysis
Sometimes our conversion requires more than 1 step.
Convert 1 Ms to hr.
Dimensional Analysis
Convert 60 miles/hour to feet/second
Other Common Chemistry Conversions…Temperature
K = C + 273
K Kelvin – SI Base unit of temp.
0 Kelvin = Absolute Zero – point at which all motion ceases!!
Questions??
What is Density?
Density = Mass / Volume
Table 3.6 (3.7 DNE) page 90
Solids & Liquids Gases
Material Density @ 20°C
Material Density @ 20°C
Gold 19.3 g/cm3 Chlorine 2.95 g/cm3
Mercury 13.6 g/cm3 Carbon dioxide 1.83 g/cm3
Lead 11.4 g/cm3 Argon 1.66 g/cm3
Aluminum 2.70 g/cm3 Oxygen 1.33 g/cm3
Table Sugar 1.59 g/cm3 Air 1.20 g/cm3
Corn syrup 1.35-1.38 g/cm3 Nitrogen 1.17 g/cm3
Water (4°C) 1.000 g/cm3 Neon 0.84 g/cm3
Corn oil 0.922 g/cm3 Ammonia 0.718 g/cm3
Ice (0°C) 0.917 g/cm3 Methane 0.665 g/cm3
Ethanol 0.789 g/cm3 Helium 0.166 g/cm3
Gasoline 0.66-0.69 g/cm3 Hydrogen 0.084 g/cm3
Metric (goes hand-in-hand with SI: The International System of Units)
Based on powers of 10Common units [with prefixes if needed]
Meter (length) Gram (mass) Second (time) Liter (volume)
If measuring a large item, use a larger unit If measuring tiny item, use a smaller unit
“Ken Hates Dates because Dates Cost MONEY!”Strategy 1: Stair-Step Method
kilo-
k hecto-
1000103
h deka-
100102
da m, L, g
10101
BasicUnit
deci-
100 d centi-
0.110-1
c milli-
0.0110-2
m
0.00110-3
How Do I Use This?
The first letter tells you which step to start on.
The first letter tells you which step to stop on.
Count the number of steps to get to where you need to stop.
If you went downstairs the decimal moves that many places to the right
How Do I Use This (cont.)?
If you went upstairs the decimal moves to the left. Fill any empty places with zeros.
If there is only one letter in the unit of measurement, then you start or stop on the base unit step. Now let’s look at our examples…..
525568 mm = ? m
.00654 km = ? m
Strategy 2: Conversion Factors (YOU MUST KNOW HOW TO DO IT THIS WAY!)
•Used to convert the same quantity of something to a new unit•Ex: 1 mL = 1 cm3 (or 1 cc)
Practice Writing Conversion Factors:
Mo metric conversion
Again, again!
Questions??