Dimensional Analysis Practice 2.54 cm = 1 inch 1 m = 1.094 yd 1760 yd = 1 mi An Italian bicycle has its frame size given as 62 cm. What is the frame size in inches? (24 in.) The length of the marathon race is approximately 26.2 mi. What is this distance in kilometers? (42.1 km)
Dimensional Analysis - warmup 1 kg = 2.2 lb., 1 kcal = 4.18 kJ, 1 m = 1.094 yd A couple of weeks ago at the gym Dr. Hart deadlifted 87.0 kg. How much is this in pounds? In ounces? (A: 191 lb, 3062 oz) In another session Dr. Hart used 81 kcal to walk 0.69 miles on the treadmill. How much is this in kJ/m? (A: 0.305 kJ/m)
Dimensional Analysis Practice 1 m = 1.094 yd 5. Convert 6.90 x 102 g/mL into cg/L. (A: 6.90 x 107 cg/L) 6. The United States will soon have high-speed trains running between Boston and New York capable of speeds up to 160 mi/hr. What is this in km/min.? (A: 4.3 km/min.)
Dimensional Analysis – numerator and denominator 1 m = 1.094 yd 7. Sound travels about 6.6 x 104 feet per minute. If we were in Australia, how far would it travel in kilometers per second? (A: 3.4 x 10-1 km/s) Convert 0.510 in./ms to km/hr. (A: 46.6 km/hr)
Density Warm Up If a metal has a mass of 154 g and has a volume of 14 cm3, what is its density? (A: 11 g/cm3) If butter has a density of 0.86 g/mL, what is the mass of 250. mL of butter? (A: 220 g) If water has a density of 0.997 g/mL what volume must 43.2 g of water have? (A: 43.3 mL) 4. A block of oak (wood) has a density of 0.774 g/cm3, mass of 113 g, length of 84.5 mm, and width of 71.0 mm. What is the thickness of this block of wood? (Hint: you may want to take 2 steps) (A: 2.43 cm or 24.3 mm)
Density and Temperature Conversions Warm Up Use the correct number of sig figs in your answer. Be sure to include units in all parts of your work. Include the equation for density for #1-3. 1. What is the density of a 125 cm3 box filled with 322 g of milk? 2. What is the volume of 20.0 g of ether if the density is 0.70 g/mL? 3. A block of balsa wood weighs 1.50 g. Its density is 0.125 g/cm3. Its length is 25.2 mm, width is 32.3 mm. What is its thickness? A temperature reading of -10.oC is what in K? 5. A temperature reading of 275 K is what in oC?
Density and Temperature Conversions Warm Up Use the correct number of sig figs in your answer. Be sure to include units in all parts of your work. Include the equation for density for #1-3. 1. What is the density of a 125 cm3 box filled with 322 g of milk? (2.58 g/cm3) 2. What is the volume of 20.0 g of ether if the density is 0.70 g/mL? (29 mL) 3. A block of balsa wood weighs 1.50 g. Its density is 0.125 g/cm3. Its length is 25.2 mm, width is 32.3 mm. What is its thickness? (1.47 cm or 14.7 mm) A temperature reading of -10.oC is what in K? (263 K) 5. A temperature reading of 275 K is what in oC? (2oC)
Sig Figs Warmup How many sig figs are in the following values: a. 2.75 mL b. 2.120 g c. 9500 mL d. 0.0123 g e. 9760. mL f. 0.005600 g Round off the values in #1 to two sig figs. 3. a. A temperature reading of –152oC is what in K? b. A temperature reading of 46 K is what in oC? 4. The density of nickel is 8.91 g/cm3. What is the thickness (height) of a sheet of nickel that has a mass of 6.52 g and an area of 32.1 mm x 32.1 mm?
Warmup How many sig figs are in the following values: a. 2.75 mL 3 sfs 2.8 mL b. 2.120 g 4 sfs 2.1 g c. 9500 mL 2 sfs 9500 mL (same) d. 0.0123 g 3 sfs 0.012 g e. 9760. mL 4 sfs 9800 mL f. 0.005600 g 4 sfs 0.0056 g Round off the values in #1 to two sig figs. 3. a. A temperature reading of –152oC is what in K? (121 K) b. A temperature reading of 46 K is what in oC? (-227oC) The density of nickel is 8.91 g/cm3. What is the thickness of a sheet of aluminum that has a mass of 6.52 g and an area of 32.1 mm x 32.1 mm? (0.0711 cm or 0.711 mm)
Warmup - More Sig Fig Practice Addition/Subtraction and Multiplication/Division Perform each of the following mathematical operations and express each result to the correct number of significant figures. 5. 9.04 mL + 8.23 mL + 21.954 mL + 81.0 mL = 6. (4.184 mm)2 = Percent error calculation: theoretical = 4.987 g/mL, your value = 4.962 g/mL)
Warmup - More Sig Fig Practice Addition/Subtraction and Multiplication/Division Perform each of the following mathematical operations and express each result to the correct number of significant figures. 5. 9.04 mL + 8.23 mL + 21.954 mL + 81.0 mL = 120.2 mL 6. (4.184 mm)2 = 17.51 mm2 Percent error calculation: theoretical = 4.987 g/mL, your value = 4.962 g/mL) A = 0.50 %