SI units International System of Units

SI Units Base Units Time – second (s) Length – meter (m) Mass – kilogram (kg) Temperature – Kelvin (K) Amount of a substance – mole (mol) Electric Current – ampere (A) Luminous intensity – candela (cd)

SI Units Derived Units Volume – cubic decimeter (dm 3 ) or liter (L) Density – kilograms/Liters (kg/L) In chemistry we will use grams/milliliter (g/mL or g/cm 3 ) There are many more derived units

Metric Prefixes Larger than the base unit Mega (M) 1 x 10 6 g = 1 Mg means 1,000,000 Kilo (k) 1 x 10 3 L = 1 kL means 1,000 Hecto (h)1 x 10 2 m = 1 hm means 100 Deca (da)1 x 10 1 g = 1 dag means 10

Metric Prefixes Smaller than the base unit deci (d) 1 g = 1 x 10 1 dg means 1/10 centi (c) 1 L = 1 x 10 2 cL means 1/100 milli (m)1 m = 1 x 10 3 mm means 1/1,000

Metric Prefixes Smaller than the base unit micro (  ) 1 g = 1 x 10 6  g means 1/1,000,000 nano (n) 1 L = 1 x 10 9 nL means 1/1,000,000,000 Angstrom (Å)1 m = 1 x Å means 1/10,000,000,000

Dimensional Analysis or the Factor Label Method 1 step problem Example – How many grams are in 3.42 kg? 1.Write down your known 3.42 kg

1 Step Problem Example – How many grams are in 3.42 kg? 2.Write down the conversion that involves your known unit on bottom and the unit you want to go to on top kg x 1000 g 1 kg 1 kg

1 Step Problem 3. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out kg x 1000 g = 3420 g 3.42 kg x 1000 g = 3420 g 1 kg 1 kg

Practice How many Liters are in 1.5 x 10 6 nL? 1.5 x 10 6 nL x 1L 1 x 10 9 nL 1.5 x 10 6 nL x 1L 1 x 10 9 nL = 1.5 x L

Practice How many milligrams are in 260 grams? 260 g x 1000 mg 1g 260 g x 1000 mg 1g = 260,000 mg

2 Step problem Example – How many milligrams are in 3.42 kg? 3.42 kg? 1.Map out your strategy. Write the unit you are starting with, the base unit you are going to, and the unit you want to end with. kg  g  mg Startbasefinal Startbasefinal

2 Step problem Example – How many milligrams are in 3.42 kg? 2. Write down your known 3.42 kg

2 Step Problem 3. Write down the first conversion. Remember, the conversion that involves your known unit on bottom and the base unit on top kg x 1000 g = 3.42 kg x 1000 g = 1 kg 1 kg

2 Step Problem 4a. Add the second conversion. Remember, the conversion that involves your known unit on bottom and the base unit you want to go to on top. Remember, the conversion that involves your known unit on bottom and the base unit you want to go to on top kg x 1000 g x 3.42 kg x 1000 g x 1 kg 1 kg

2 Step Problem 4b. Add the second conversion. Remember, the conversion that involves your base unit on bottom and the unit you want to go to on top kg x 1000 g x 1000 mg = 1 kg 1g 1 kg 1g

2 Step Problem 5. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out kg x 1000 g x 1000 mg 3.42 kg x 1000 g x 1000 mg 1 kg 1g 1 kg 1g = 3.42 x 10 6 mg = 3.42 x 10 6 mg

Practice How many milligrams are in 260 kilograms? kg  g  mg 260 kg x 1000 g x 1000 mg 260 kg x 1000 g x 1000 mg 1kg 1 g 1kg 1 g = 2.6 x 10 8 mg

Practice How many megameters are in 50. Angstroms? Å  m  Mm 50 Å x 1m x 1Mm 50 Å x 1m x 1Mm 1 x Å 1 x 10 6 m 1 x Å 1 x 10 6 m = 5 x Mm

English to Metric Prefixes Length 2.54 cm = 1 in Mass454 g = 1 lb Volume1 L = 1.06 qt

Multiple Step problem Some English to Metric Calculations will have multiple steps. Ex. How many ft are in 240 nm? 1.Map out your strategy. Write the unit you are starting with, the bridge between the two systems, and the unit you want to end with. nm  m  cm  in  ft Startbasebridgefinish

Multiple Step problem Some English to Metric Calculations will have multiple steps. Ex. How many ft are in 240 nm? 2. Fill in any missing conversions.

Multiple Step problem Example – How many ft are in 240 nm? 1.Write down your known 240 nm

Multiple Step Problem 2.Write down the first conversion. Remember, the conversion that involves your known unit on bottom and the base unit on top. 240 nm x 1 m = 240 nm x 1 m = 1 x 10 9 nm 1 x 10 9 nm

Multiple Step Problem 3.Add the other conversions. 240 nm x 1 m x 100 cm x 1 in x 1 ft = 1 x 10 9 nm 1m 2.54 cm 12 in 1 x 10 9 nm 1m 2.54 cm 12 in

Multiple Step Problem 4. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out. Your final answer should have the same amount of sig figs as the number you started with. 240 nm x 1 m x 100 cm x 1 in x 1 ft = 240 nm x 1 m x 100 cm x 1 in x 1 ft = 1 x 10 9 nm 1m 2.54 cm 12 in = 7.9 x ft = 7.9 x ft

Practice How many milligrams are in 12 ounces? How many milligrams are in 12 ounces? oz  lb  g  mg 12 oz x 1 lb x 454 g x 1000mg 12 oz x 1 lb x 454 g x 1000mg 16 oz 1 lb 1g = 3.4 x 10 5 mg = 3.4 x 10 5 mg

Practice How many miles are in 17.0 km? How many miles are in 17.0 km? km  m  cm  in  ft  mi 17.0 km x 1000 m x 100cm x 1in___ x 1 ft x 1 mi__ 17.0 km x 1000 m x 100cm x 1in___ x 1 ft x 1 mi__ 1km 1 m 2.54 cm 12 in 5280 ft = 10.6 mi = 10.6 mi

Density Density = Mass/Volume d = m/v m = dv v = m/d

Density Example: What is density of an object with a mass of 10.0 g and a volume of 2.0 cm 3 ? 1. Write down your knowns on the left and your formula on the right. left and your formula on the right.

Density Example: What is density of an object with a mass of 10.0 g and a volume of 2.0 cm 3 ? KnownsFormula M = 10.0g d = m/v V = 2.0 cm 3 D = ?

Density 2. Plug in and solve. Include units on all numbers.

Density Example: What is density of an object with a mass of 10.0 g and a volume of 2.0 cm 3 ? KnownsFormula M = 10.0g d = m/v V = 2.0 cm 3 D = ? D = 10.0 g / 2.0 cm 3 = 5.0 g/cm 3 = 5.0 g/cm 3

Density Example: What is the mass of an object with a density of 4.0 g/mL and a volume of 0.5 mL? KnownsFormula m = ? m = dv v = 0.5 mL d = 4.0 g/mL m = 4.0 g/mL x 0.5 mL = 2 g = 2 g

Density Example: What is the volume of an object with a density of 4.0 g/mL and a mass of 0.5 g? KnownsFormula m = 0.5 g v = m/d v = ? d = 4.0 g/mL v= 0.5g / 4.0 g/mL = mL = mL = 0.1 mL = 0.1 mL

Practice Example: What is the volume of an object with a density of 12.0 g/mL and a mass of 36.0 g? KnownsFormula m = 36.0 g v = m/d v = ? d = 12.0 g/mL v= 36.0g / 12.0 g/mL = 3.00 mL = 3.00 mL

Practice Example: What is the mass of an object with a density of 4.0 g/mL and a volume of 2.5 mL? KnownsFormula m = ? m = dv v = 2.5 mL d = 4.0 g/mL m = 4.0 g/mL x 2.5 mL = 10. g = 10. g

Practice Example: What is density of an object with a mass of 5.0 g and a volume of 2 cm 3 ? KnownsFormula m = 10.0g d = m/v v = 2.0 cm 3 d = ? D = 5.0 g / 2 cm 3 = 2.5 g/cm 3 = 2.5 g/cm 3 = 3 g/cm 3 = 3 g/cm 3

Area Length x width Ex. What is the area of a piece of paper 18.0 cm x 22.0 cm? 18.0 cm x 22.0 cm?

Volume Length x width x height Ex. What is the volume of a wood of paper 27.0 cm x 14.0 cm x 8.0 cm? 27.0 cm x 14.0 cm x 8.0 cm?

Converting between units with Area and Volume Ex. What is the area of a piece of paper 7.0 cm x 9.0 cm? 7.0 cm x 9.0 cm? What is the area in meters?

Ex. What is the area of a piece of paper 7.0 cm x 9.0 cm? 7.0 cm x 9.0 cm? What is the area in feet?

Ex. What is the volume of a piece of metal 57.0 mm x 9.0 mm x 12 mm? 57.0 mm x 9.0 mm x 12 mm? What is the volume in kilometers?

Ex. What is the volume of a piece of metal 57.0 mm x 9.0 mm x 12 mm? 57.0 mm x 9.0 mm x 12 mm? What is the volume in kiloliters?