Warm-up (IB): Do the following metric conversions showing dimensional analysis 62.262 km to m 44.721...
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Transcript of Warm-up (IB): Do the following metric conversions showing dimensional analysis 62.262 km to m 44.721...
Warm-up (IB):Do the following metric
conversions showing dimensional analysis
62.262 km to m
44.721 mm to km
2.15 cm to mm
Scientific NotationWrite out 600 sextillion out on
your paper (hint: that is a 600 with 21 zeros behind it.
600,000,000,000,000,000,000,000
Would you want to write that number out 20 times on your paper when doing calculations? This number is a common number in chemistry.
Scientific NotationThere are 2 reasons why we have
scientific notation◦1. It is easier to write very large and vary
small numbers.◦2. It allows us to convey numbers easily
with the correct number of sig figs.Format: Numbers are written as a
product of a number between 1 and 10, times the number 10 raised to a power.◦Ex. 6.02x1023 or 6.02x10^23
Scientific notationA negative exponent for a
number means that number is less than 1.
A positive exponent for a number means that number is greater than 1.
Scientific NotationConverting decimal to Scientific notation
◦ RNLP- “Registered Nurses Love Patients”, Right for negative and left for positive
◦ 1090000 1.09x10^6
◦ 0.000462 4.62x10^-4
Converting Scientific notation to decimal◦ Use opposite rules for RNLP◦ 5.92x10^3
5920
◦ 8.2x10^-5 0.000082
PracticeConvert to Scientific notation
◦ 23600a.) 2.36x10^-2 b.) 2.36x10^-4 c.) 2.36x10^2 d.) 2.36x10^4◦ 0.01054a.) 1.054x10^-2 b.) 1.054x10^-4 c.) 1.054x10^2 d.) 1.054x10^4
Convert to decimal notation◦ 8.15x10^4a.) 0.000815 b.) 81500◦ 6.046x10^-2a.) 0.06046 b.) 604.6
Extra Practice
Convert the following to Scientific Notation
4230100 0.00000032 400
Convert the following to Decimal Notation
6.02x10^4 5.21x10^-3 8x10^-6
4.2301x10^6 3.2x10^-7 4x10^2
6020 0.00521 0.000008
Warm-up:Solve the following problems.
◦ 3 x 4 4 3
◦6 x 1 x 88 6 2
◦cm x in x ft = cm in
◦g x mol x atoms = g mol
Dimensional AnalysisAlso called unit conversionPurpose: convert units of one
thing to the next◦Ex. Convert feet to inches,
kilometers to meters, etc.How it works
◦Dimensional analysis is finding a conversion factor which equals one and using that to switch units
ExamplesConvert 2 feet to inches.
◦First need to know how many inches in a foot.
◦1 foot = 12 inches◦2 ft x 12in =
1ftConvert 45 cm to meters
◦First need to know how many cm in a meter◦1 meter = 100 cm◦45cm x 1m =
100cm
1000 m = 1 km100 cm = 1 m length
problems1000 mm = 1 m
1000 L = 1 kL100 cL = 1 L volume problems1000 mL = 1 L
1000 g = 1 kg100 cg = 1 g mass problems1000 mg = 1 g
ExamplesConvert your age in years to seconds.
◦ First need to know the path you’re going to take.◦ We know how many days are in a year (365d =
1yr)◦ We know how many hours are in a day (24hr = 1
day)◦ We know how many minutes are in an hour
(60min = 1 hr)◦ We know how many seconds are in a min (60s =
1min)◦ Now put it together starting with what you know.
◦ 16 yrs x x x x =1yr365d 24hr 60min 60s
1min1hr1dIDC
Dimensional Analysis Examples15.2 days into hours
◦24.0 hours = 1 day ◦A) 1 day B) 24 hrs
24 hrs 1 day
Dimensional Analysis Examples30.0 centimeters into inches
◦1 inch = 2.54 centimeters ◦A) 1 in. B) 2.54 cm
2.54 cm 1 in.16 meters/second into miles/hour
◦1 meter/second = 3.60 km/h ◦1 km/h = 0.621 mi/h ◦A) 1 m/s B) 3.6 km/h
3.6 km/h 1 m/s◦A) 1 km/h B) 0.621 mi/h
0.621 mi/h 1 km/h
Dimensional Analysis Examples2.1 light years into feet
◦1 light-year = 9.46 x 1015 meters ◦1 foot = 0.31 meters ◦A) 1 lyr B) 9.46x10^15 m
9.46x10^15 m 1 lyr◦A) 1 ft B) 0.31 m
0.31 m 1 ft
Dimensional Analysis Examples14.6 kilometers into inches
◦1 km = 0.621 miles ◦1 mile = 5280 feet ◦1 foot = 12 inches ◦A) 1 km B) 0.621 miles
0.621 miles 1 km◦A) 1 mile B) 5280 ft
5280 ft 1 mile◦A) 1 ft B) 12 in.
12 in. 1 ft
Warm-up:Without a calculator solve the
following problems◦1312 x 1 x 1000
100 1◦546 x 1 x 1 x 1 x 100 x 100
100 10 1000 1 1
2 types of measurement systemsEnglish system
◦System is based off of the kings◦The system used to change for every new
king◦Now the system is stable but is confusing to
convertMetric system
◦Developed to reduce the problems of conversion
◦System is used by the majority of the world◦The whole system is based off of powers of
10
Metric SystemThe metric system is based on a base
unit that corresponds to a certain kind of measurement
Length = meter (m) Volume = Liter (L) Weight (Mass) = gram (g)
Prefixes plus base units make up the metric system ◦ Example:
Centi + meter = Centimeter Kilo + liter = Kiloliter
Metric SystemThe three prefixes that we will use the
most are:◦kilo◦centi◦Milli
What you need to know is what those prefixes mean. ◦Kilo (k) = 1000◦Centi (c) = 1/100◦Milli (m) = 1/1000
Metric Prefixes
1000mg
1g
1000mL 1L
1000mm
1m
1000g 1kg
1000L 1kL
1000m 1km
100cg 1g
100cL 1L
100cm 1m
Conversion cards FRONT, use reciprocal for back
Metric conversionsLets start by doing a simple conversion.Convert 2 kilometers into metersWe start with what we know
◦2 km x ◦We now need to find a relationship between
km to m.◦We know that kilo = 1000. So a km = 1000m◦We can use that as a conversion factor to
solve◦2 km x 1000m =
1km
Metric conversionsLets do a 2 step conversion.Convert 1534 millimeters into kilometers We start with what we know
◦ 1534 mm x x ◦ We now need to find a relationship between mm to
km.◦ We know that milli = 1/1000. So a mm =1/1000m or
1000mm = 1m◦ We can then convert that meter into km by kilo =
1000. So a km = 1000m◦ We can then use the information as conversion
factors◦ 1534 mm x 1m x 1km =
1000mm 1000m
40ml=____ L
5000 L=____ kL
8 g=____ kg
12000 L=____ kL
50 mg=____ g
40mL x 1 L = 0.04 L 1000mL
5000 L x 1 kL = 5 kL 1000 L
8 g x 1 kg = 0.008 kg 1000 g
12000 L x 1 kL = 12 kL 1000 L
50mg x 1 g = 0.05 L 1000mg
4000 L=___ kL 400 cm=___ m
20 ml=___ kL
7000 ml=___ L 7 cm=___ mm
400 cm x 1 m = 4 m 100cm
4000 L x 1 kL = 4 kL 1000 L
20 ml x 1 L x 1 kL = 0.00008 kL 1000 mL 1000 L
7000 L x 1 L = 7 L 1000 mL
7cm x 1 m x 1000mm = 70 mm 100cm 1m