Warm-up (IB): Do the following metric conversions showing dimensional analysis km to m mm to km 2.15 cm to mm

Scientific Notation Write 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 Notation There 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. 6.02x10 23 or 6.02x10^23

Scientific notation A 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 Notation Converting decimal to Scientific notation ◦ RNLP- “Registered Nurses Love Patients”, Right for negative and left for positive ◦  1.09x10^6 ◦  4.62x10^-4 Converting Scientific notation to decimal ◦ Use opposite rules for RNLP ◦ 5.92x10^3  5920 ◦ 8.2x10^-5 

Practice Convert to Scientific notation ◦ a.) 2.36x10^-2 b.) 2.36x10^-4 c.) 2.36x10^2 d.) 2.36x10^4 ◦ a.) 1.054x10^-2 b.) 1.054x10^-4 c.) 1.054x10^2 d.) 1.054x10^4 Convert to decimal notation ◦ 8.15x10^4 a.) b.) ◦ 6.046x10^-2 a.) b.) 604.6

Extra Practice Convert the following to Scientific Notation Convert the following to Decimal Notation 6.02x10^45.21x10^-38x10^ x10^63.2x10^-74x10^

Warm-up: Solve the following problems. ◦ 3 x ◦ 6 x 1 x ◦ cm x in x ft = cm in ◦ g x mol x atoms = g mol

Dimensional Analysis Also called unit conversion Purpose: 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

Examples Convert 2 feet to inches. ◦ First need to know how many inches in a foot. ◦ 1 foot = 12 inches ◦ 2 ft x 12in = 1ft Convert 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 km 100 cm = 1 mlength problems 1000 mm = 1 m 1000 L = 1 kL 100 cL = 1 Lvolume problems 1000 mL = 1 L 1000 g = 1 kg 100 cg = 1 gmass problems 1000 mg = 1 g

Examples Convert 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 = 1yr 365d24hr60min60s 1min1hr1d IDC

Dimensional Analysis Examples 15.2 days into hours ◦ 24.0 hours = 1 day ◦ A) 1 day B) 24 hrs 24 hrs 1 day

Dimensional Analysis Examples 30.0 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 = mi/h ◦ A) 1 m/s B) 3.6 km/h 3.6 km/h 1 m/s ◦ A) 1 km/h B) mi/h mi/h 1 km/h

Dimensional Analysis Examples 2.1 light years into feet ◦ 1 light-year = 9.46 x 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 Examples 14.6 kilometers into inches ◦ 1 km = miles ◦ 1 mile = 5280 feet ◦ 1 foot = 12 inches ◦ A) 1 km B) miles miles 1 km ◦ A) 1 mile B) 5280 ft 5280 ft 1 mile ◦ A) 1 ftB) 12 in. 12 in. 1 ft

Warm-up: Without a calculator solve the following problems ◦ 1312 x 1 x ◦ 546 x 1 x 1 x 1 x 100 x

2 types of measurement systems English 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 convert Metric 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 System The 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 System The 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 conversions Lets start by doing a simple conversion. Convert 2 kilometers into meters We start with what we know ◦ 2 km x ◦ We now need to find a relationship between km to m. ◦ We know that kilo = So a km = 1000m ◦ We can use that as a conversion factor to solve ◦ 2 km x 1000m = 1km

Metric conversions Lets 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 = 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 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 = kg 1000 g 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 = kL 1000 mL 1000 L 7000 L x 1 L = 7 L 1000 mL 7cm x 1 m x 1000mm = 70 mm 100cm 1m