Topic -1 Quantities and Units

Magnitude Unit

Ascorbic Acid or Vitamin C

500 mg

Bacteria

Quantities Length Mass Time Mole Volume

SI (International System) Base Units Quantity Written Unit Unit Symbol Length metre m Mass gram g Time second s Amount of substance mole mol volume litre L

What are Metric Conversions? Sometimes we need to change from one measurement to another. This is usually done because the unit that is used is either too big or too small for that type of measurement.

Sometimes the number is too big for the unit being measured. 525,568 millimeters Sometimes the number is too big for the unit being measured.

Sometimes the number is too small for the unit being measured .00654 km Sometimes the number is too small for the unit being measured

1 school 250 students 2 bags each student Each bag 4 pockets Each pocket 2 notebooks Each notebook 39 pages How many total pages?

2.5 cm Magnitude Prefix Unit Exponent Symbol Name name 2.5 10-2 c centi m meter

Workbook Page 19 Question 11

Confusions da and d mol and mole M and m G and g t cm3 and dm3

Workbook Page 19 Question 12

Workbook Page 19 Question 13-14

Metric Conversions Changing prefix

Ladder Method 1 2 3 KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit Meters Liters Grams CENTI 0.01 Unit MILLI 0.001 Unit How do you use the “ladder” method? 1st – Determine your starting point. 2nd – Convert to basic Unit. 3rd – Convert to required Unit 4 km = _________ m

Conversion Practice Try these conversions using the ladder method. 1000 mg = _______ g 1 L = _______ mL 160 cm = _______ mm 14 km = _______ m 109 g = _______ kg 250 m = _______ km Compare using <, >, or =. 56 cm 6 m 7 g 698 mg

Very small pm picometer x 103 x 103 ηm nanometer x 103 μm micrometer x 103 mm millimeter x 103 m meter x 103 km kilometer x 103 Mm megameter x 103 Gm gegameter Very big Tm terameter

You should also know x 101 mm millimeter x 102 cm centimeter m meter

1. Convert 1.23 x 1012 Mm to m? 1.23 x 1012 Mm x 1 x 106 m 1 Mm Write the starting number and units

2. Convert 6.5 x 10-6 m to nm? 6.5 x 10-6 m x 1 x 103 mm x 1 x 103 μm x 1 x 103 nm 1 m 1 mm 1 μm = 6.5 x 103 nm

3. Convert 6.5 x 106 nm to m? 6.5 x 106 nm x 1 x 10-9 m nm

4. Convert 5.88 x 108 μm to km 5.88 x 108 μm x 1 x 103 m x 1 km 1 μm

5. Convert 65 m2 to mm2 65 m2 x 1 x 103 ( )2 mm 2 2 1 m ( )2 mm 2 2 1 m = 6.5 x 107 mm2

6. Convert 875 mm3 to m3 875 mm3 x 1 m 3 3 ( )3 1 x 103 mm ( )3 1 x 103 mm = 8.75 x 10-7 m3

Metric Conversion Challenge Write the correct abbreviation for each metric unit. 1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____ 2) Meter _____ 5) Millimeter _____ 8) Centimeter _____ 3) Gram _____ 6) Liter _____ 9) Milligram _____ Try these conversions, using the ladder method. 10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm 11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km 12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg 13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm 14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g

Conversion Factors Examples of Conversion Factors 12 in = 1 ft 100 cm = 1 m 12 in or 1 ft 1 ft 12 in 100 cm or 1 m 1 m 100 cm Every relationship can give two conversion factors that are the inverses of each other.

Dimensional Analysis - One Conversion Factor Example: A lab bench is 175 inches long. What is its length in feet?

Dimensional Analysis - One Conversion Factor Example: A lab bench is 175 inches long. What is its length in feet? Conversion factor: 12 in or 1 ft 1 ft 12 in. Given: 175 in. Find: Length (ft) ft = 175 in X 1 ft = 14.583333 ft = 14.6 ft 12 in

Dimensional Analysis - One Conversion Factor Example: A marble rolled 50.0 mm. How many meters did it roll?

- One Conversion Factor Example: A marble rolled 50.0 mm. How many meters did it roll? Conversion factor: 1000 mm or 1 m 1 m 1000 mm Given: 50.0 mm Find: dist. (m) m = 50.0 mm X 1 m = 0.05 m = 0.0500 m 1000 mm

Dimensional Analysis - One Conversion Factor Example: In Germany, a salesman drove at 185 km/hr. What was our speed in mi/hr?

One Conversion Factor Example: In Germany, a salesman drove at 185 km/hr. What was our speed in mi/hr? Conversion factor: 1.609 km or 1 mi 1 mi 1.609 km Given: 185 km/hr Find: mi/hr mi = 185 km X 1 mi = 114.97825 mi hr hr 1.609 km hr Speed = 115 mi/hr

Nonmetric Conversions

= 2.148 x 109 mL Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 1. 2.148 ML to mL   2.148 ML x 1000 kL x 1000 L x 1000 mL = 2.148 x 109 mL 1 ML 1kL 1 L

Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 2. 0.025 ton to mg   0.025 ton x 2000 lb x 1 kg x 1000 g x 1000 mg = 2.3 x 107 mg 1 ton 2.21 lb 1 kg 1 g Round to 2 sig figs

Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 3. 256 oz to tons 256 oz x 1 lb x 1 ton = 8.00 x 10-3 tons 16 oz 2000 lb Round to 3 sig figs

= 3.35 x 10-2 gal Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 4. 152 mL to gal 152 mL x 1 L x 1 gal = 3.35 x 10-2 gal 1000 mL 4.54 L Round to 3 sig figs

Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 5. 37 mi/gal to km/L 37 mi 1 gal x 1.61 km x 1.00 gal = 13 km/L 1.00 mi 4.54 L

Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 6. 22.4 km/L to mi/gal 22.4 km x 1.00 mi x 4.54 L = 63.2 mi/gal 1 L 1.61 km 1 gal

x 4.54 L x 1.00 mi Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 7. 15.2 mi/gal to L/km x 4.54 L x 1.00 mi 1 gal = 1.86 x 10-1 L/km 15.2 mi 1.00 gal 1.61 km Invert so that volume is on top!

Given that: 2.21 lb = 1.00 kg 4.54 L = 1.00 gal 1.00 atm = 101.3 kPa 1.61 km = 1.00 mile 14 lb = 1 stone 2000 lb = 1 ton 16 oz = 1 lb 8. 25.6 L/km to mi/gal   1 km x 4.54 L x 1.00 mi = 0.110 mi/gal 25.6 L 1.00 gal 1.61 km Invert so that distance is on top!

9. Convert 46 m2 to mm2 46 m2 x 1 x 103 ( )2 mm 2 2 1 m = 4.6 x 107 mm2

10. Convert 269 mm3 to m3 269 mm3 x 1 m 3 3 ( )3 1 x 103 mm ( )3 1 x 103 mm = 2.69 x 10-7 m3

Workbook Page 21 Questions 16-17

Derived Quantities  

Density  

Density = mass volume The unit for density is either g/mL or g/cm3. 1 mL = 1 cm3

Given that a 2. 44 cm3 sample of an element has a mass of 47. 14 g Given that a 2.44 cm3 sample of an element has a mass of 47.14 g. Determine the density and the element. Density = mass volume D = 47.14 g 2.44 cm3 D = 19.3 g/cm3

Determine the volume of a 60 Determine the volume of a 60.50 g sample of a liquid with a density of 1.56 g/mL. 60.50 g x 1 mL = 38.8 mL 3 sig. figs 1.56 g

Do some research to find density of lead. 3. Determine the mass of a 85.0 cm3 sample of lead. Do some research to find density of lead. Density = 11.34 g/cm3 85.0 cm3 x 11.34 g = 964 g 3 sig. figs. 1 cm3

4. Determine the volume in mm3 of a 15. g sample of lead. Density = 11.34 g/cm3 15. g x 1 cm3 x 1000 mm3 = 1.3 x 103 mm3 11.34 g 1 cm 3

5. Determine the mass of a 208 mm3 sample of lead. Density = 11.34 g/cm3 208 mm3 x 1 cm3 x 11.34 g = 2.36 g 1000 mm3 1 cm3

6. What volume of sample of lead (11. 34 g/mL) has the same mass as 45 6. What volume of sample of lead (11.34 g/mL) has the same mass as 45.00 mL of Ag (19.32 g/mL). 45.00 mL x 19.32 g x 1 mL = 76.67 mL 1 mL 11.34 g

6. Determine the volume in mm3 of a 1.0 x 10-8 ton sample of silver. Density = 10.5 g/cm3 1.0 x 10-8 ton x 2000 lbs x 1 kg x 1000 g x 1 cm3 x 1 x 103 mm3 = 0.86 mm3 1 ton 2.21 lbs 1 kg 10.5 g 1 cm3 Density of Coke