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