Quantitative Analysis
-
Upload
ferdinand-delaney -
Category
Documents
-
view
22 -
download
1
description
Transcript of Quantitative Analysis
Quantitative Analysis
English-Metric Conversions&
Scientific Notation
• Quantity – something that has magnitude, size, or amount (length, mass, volume)
• Unit – a quantity adopted as a standard of measurement (meter, kilogram, liter)
• Conversion Factor – ratio equating two different units; used to convert from one unit to the other
Density• Mass divided by volume
for any substance• Often used to identify a
substance• More dense objects sink
to the bottom• Common conversion
factor
International System of Units (or SI units) –measurement system used by the scientific community worldwide
Base Units are: meters, kilograms, seconds,and kelvins
Length Conversions
Metric to Metric
1000 millimeters (mm) = 1 meter (m)
100 centimeters (cm) = 1 meter (m)
1000 meters (m) = 1kilometer(km)
English to English
1 mile (mi) = 5280 feet (ft)
1 yard (yd) = 3 feet (ft)
1 foot (ft) = 12 inches (in)
Metric to English
2.54 cm = 1 in
Practice
Convert 12350 millimeters to miles
Mass – the amount of matter in a
substance
– doesn’t change
Weight – a force due to gravity
-- can change depending on
location
Mass & Weight Conversions
Metric to Metric
1000 milligrams (mg) = 1 gram (g)
100 centigrams (cg) = 1 gram (g)
1000 grams (g) = 1 kilogram (kg)
English to English
16 ounces (oz) = 1 pound (lb)
2000 pounds (lb) = 1 ton
Metric to English
453.59 g = 1 lb
Practice
Convert 13.5 kilograms to ounces
Volume Conversions
Metric to Metric
1000 milliliters (mL) = 1 liter (L)
1000 liters (L) = 1 kiloliter (kL)
1 cubic centimeter (cm3) = 1 milliliter (mL)
English to English
1 gallon (gal) = 4 quarts (qt)
1 cubic foot (ft3) = 7.475 gallons (gal)
Metric to English
1 L = 1.06 qt
PracticeConvert 6.75 cubic feet to cubic
centimeters
Time Conversions Universal Units
60 seconds (sec) = 1 minute (min)
60 minutes (min) = 1 hour (hr)
24 hours (hr) = 1 day
365 days = 1 year (yr)
7 days = 1 week (wk)
PracticeConvert 35.6 days to seconds
Significant Figures
How many digits does my answer have to have?!
It depends on how accurate your measurements are.
Nonzero digits are always significant
46.3 m has ___ sig. figs.
6.295 g has ___ sig. figs.
Zeros between nonzero digits are significant
40.7 L has ___ sig. figs.
87009 km has ___ sig. figs.
Zeros in front of nonzero digits are not significant
0.009587 m has ___ sig. figs.
0.0009 kg has ___ sig. figs.
Zeros at the end of a number AND to the right of a decimal point are
significant
85.00 g has ___ sig. figs.
9.070000000 cm has ___ sig. figs.
123000.00 mL has ___ sig. figs.
Zeros at the end of a number that does not have a decimal point are not
significant
8500 g has ___ sig. figs.
9070000000 cm has ___ sig. figs.
Rules for using Sig. Figs.
Where do I round off?
1. Multiplication and division: answer has same number of sig figs as the number in problem with fewest sig. figs.
12.4 x 7.943 =
246.83 / 26 =
2. Addition and subtraction: answer can only be as accurate as the least accurate number in problem (line up your numbers)
3.95 54.638
2.879 -31.22
+213.6
3. Problems with both addition (or subtraction) and multiplication (or division): round off after each operation
Converting 2 Unit Numbers
1. The number always goes with the unit on top
2. Convert top unit first, then bottom unit
Convert 970 kilometers per hour to feet per second
(970 km/hr ? ft/sec )
2 Unit Numbers as Conversion Factors
1. Start with the number that contains only one unit
2. Use the number that contains 2 units as a conversion factor in the middle of the problem
Example
On an average day the Delaware River flows past the Delaware Memorial Bridge at a rate of 7000 gal/sec .
How many minutes would it take for 6800 kL of water to pass the Delaware Memorial Bridge?
Scientific Notation Convenient way to express long numbers
Rule #1 – only one non-zero digit to left of decimal
Rule #2 – Large numbers have positive exponent, small numbers have negative exponent
Rule #3 – move decimal right, subtract from exponent
Rule #4 – move decimal left, add to exponent
PracticeConvert to Scientific Notation:
7538000 =
0.0000000000000896 =
Convert to regular numbers:
6.97 x 10-7 =
3.21 x 1023 =
Correct the following Scientific Notation:
0.0235 x 10-13 =
5635 x 10-9 =
32569 x 105 =
0.000054 x 1035 =
Multiplying
Multiply numbers, add exponents, correct Sci. Not.
(3.1 x 103) (5.01 x 104)
Multiplying
Multiply numbers, add exponents, correct Sci. Not.
(3.1 x 103) (5.01 x 104)
(3.1 x 5.01) x 103+4
Multiplying
Multiply numbers, add exponents, correct Sci. Not.
(3.1 x 103) (5.01 x 104)
(3.1 x 5.01) x 103+4
15.531 x 107
Multiplying
Multiply numbers, add exponents, correct Sci. Not.
(3.1 x 103) (5.01 x 104)
(3.1 x 5.01) x 103+4
15.531 x 107
1.5531 x 108
Multiplying
Try These:
(5.13 x 10-3) (9.87 x 1017)
(6.58 x10-8) (1.32 x10-14)
DividingDivide numbers, subtract exponents,
correct Sci. Not.
7.63 x 103 =
8.62 x 104
DividingDivide numbers, subtract exponents,
correct Sci. Not.7.63 x 103
= 7.63 x 103-4
8.62 x 104 8.62
DividingDivide numbers, subtract exponents,
correct Sci. Not.7.63 x 103
= 7.63 x 103-4
= 0.885 x 10-1
8.62 x 104 8.62
DividingDivide numbers, subtract exponents,
correct Sci. Not.7.63 x 103
= 7.63 x 103-4
= 0.885 x 10-1
8.62 x 104 8.62
0.885 x 10-1 = 8.85 x 10-2
DividingTry These, but…
…watch out for double negatives when subtracting!
5.32 x 10-13 1.49 x 10-5 3.21 x 107
1.25 x 10-47 7.25 x 109 6.11 x 10-11
Conversions with Sci. Not.
Convert 3.24 x 108 kilometers per hour to feet per second
(3.24 x 108 km/hr ? ft/sec )