Question

physical science dimensional analysis ws1 convert the following. be sure to include units and show your work. 1. 5.0 km to miles 2. 36 in to m 3. 150 lb to kg 4. 1.0 gal to l 5. 2.39×10² miles to km 6. 87 cm to ft 7. 550 ml to quarts mass: 1 kg = 2.205 lb, 1 lb = 453.6 g = 16 oz, 1 metric ton = 1000 kg, 1 amu = 1.660539×10⁻²⁷ g length: 1 m = 39.37 in = 10¹⁰ angstroms (å), 1 ft = 12 in, 1 in = 2.54 cm, 1 mile = 5280 ft = 1.609 km, 1 yard = 3 ft volume: 1 cm³ = 1 ml, 1 m³ = 1000 l = 35.315 ft³, 1 m³ = 264.17 gal, 1 l = 1.057 qt, 1 oz = 29.57 ml, 1 ft³ = 7.481 gal = 28.317 l, 1 barrel (bbl) = 42 gal, 1 gal = 4 qt = 8 pints = 16 cups, 1 cup = 16 tbsp = 48 tsp, 1 tsp = 4.93 ml energy: 1 j = 1 n·m = 1 kg·m/s² = 10⁷ erg, 1 cal = 4.184 j, 1 btu = 1055 j, 1 kw·hr = 3,600,000 j power: 1 w = 1 j/s = 0.001341 hp temperature: °f = 9/5 °c + 32, °c = 5/9 (°f - 32) pressure: 1 atm = 14.696 psi = 101.325 kpa = 760 torr = 760 mm hg = 1.01325 bars, 1 pa = 1 n/m²

Explanation:

Step1: Recall conversion factor for km to miles

We know that 1 mile = 1.609 km. So to convert 6.0 km to miles, we divide by the conversion - factor.
$6.0\mathrm{km}\times\frac{1\mathrm{mile}}{1.609\mathrm{km}}\approx3.73\mathrm{miles}$

Step2: Recall conversion factor for inches to meters

Since 1 in = 2.54 cm and 1 m = 100 cm, then 1 in=$\frac{2.54}{100}$m. To convert 36 in to m, we multiply 36 by the conversion factor.
$36\mathrm{in}\times\frac{2.54\mathrm{cm}}{1\mathrm{in}}\times\frac{1\mathrm{m}}{100\mathrm{cm}} = 0.9144\mathrm{m}$

Step3: Recall conversion factor for pounds to kilograms

We know that 1 kg = 2.205 lb. So to convert 150 lb to kg, we divide by the conversion - factor.
$150\mathrm{lb}\times\frac{1\mathrm{kg}}{2.205\mathrm{lb}}\approx68.039\mathrm{kg}$

Step4: Recall conversion factor for gallons to liters

We know that 1 gal = 3.785 L. So 1.0 gal = 3.785 L.

Step5: Recall conversion factor for miles to km

Since 1 mile = 1.609 km, to convert $2.39\times10^{5}$ miles to km, we multiply by the conversion factor.
$(2.39\times10^{5}\mathrm{miles})\times\frac{1.609\mathrm{km}}{1\mathrm{mile}}=2.39\times1.609\times10^{5}\mathrm{km}\approx3.84551\times10^{5}\mathrm{km}$

Step6: Recall conversion factor for cm to inches and inches to feet

Since 1 in = 2.54 cm and 1 ft = 12 in. First convert 87 cm to inches: $87\mathrm{cm}\times\frac{1\mathrm{in}}{2.54\mathrm{cm}}\approx34.252\mathrm{in}$. Then convert inches to feet: $34.252\mathrm{in}\times\frac{1\mathrm{ft}}{12\mathrm{in}}\approx2.854\mathrm{ft}$

Step7: Recall conversion factor for mL to quarts

Since 1 L = 1000 mL and 1 L = 1.057 qt. First convert 550 mL to L: $550\mathrm{mL}\times\frac{1\mathrm{L}}{1000\mathrm{mL}} = 0.55\mathrm{L}$. Then convert L to quarts: $0.55\mathrm{L}\times\frac{1.057\mathrm{qt}}{1\mathrm{L}}\approx0.58135\mathrm{qt}$

Answer:

1. 3.73 miles
2. 0.9144 m
3. 68.039 kg
4. 3.785 L
5. $3.84551\times10^{5}$ km
6. 2.854 ft
7. 0.58135 qt