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Dimensional Analysis
Conversions&
Scientific Notation
• Quantity – is something that has magnitude, size, or amount (length, mass, volume) “something that is measured”
• Unit – a standard of measurement (meter, kilogram, liter) “how something is measured”
• Conversion Factor – ratio or fraction equating two different units; used to convert from one unit to the other
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)
Metric to English
2.54 cm = 1 in
PracticeConvert 70 inches to centimeters
Convert 1235 centimeters to feet
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)
Metric to English
453.59 g = 1 lb
PracticeConvert 4 pounds to grams
Convert 13.5 kilograms to pounds
Volume Conversions
Metric to Metric
1000 milliliters (mL) = 1 liter (L)
1000 liters (L) = 1 kiloliter (kL)
1 cubic centimeter (cm3) = 1 milliliter (mL)
Metric to English
1 L = 1.06 qt
PracticeConvert 15 liters to quarts
Convert 6.75 quarts to milliliters
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)
PracticeConvert 35.6 days to hours
Convert 15000 seconds to days
Density• Mass divided by volume
for any substance• Often used to identify a
substance• More dense objects sink
to the bottom• Common conversion
factor
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 108 =
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 103) (9.87 x 1017)
(6.58 x108) (1.32 x1014)
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
5.32 x 1047 1.49 x 109 3.21 x 107
1.25 x 1013 7.25 x 105 6.11 x 1011
Conversions with Sci. Not.
Convert 3.24 x 108 kilometers per hour to feet per second
(3.24 x 108 km/hr ? ft/sec )