English-metric conversions. Use correct significant figures. 1. Convert 1760 yards to miles. 2. Convert 1.289 x 10^7 miles to meters. 3. Convert 850 kilocalories to kilojoules. 4. Convert 125 inches to millimeters. 5. Convert 828.5 pounds to kilograms. 6. Calculate using the density equation: Density (grams/ml) = mass (grams) / volume (ml). a. A substance has a mass of 100.0 grams and a volume of 900.0 milliliters. Calculate the density in g/ml. b. A substance weighs 79.1 grams. Its density is 0.790 g/ml. Calculate the volume in liters. 7. Calculate the following metric-metric conversions: a. Convert 10.0 meters to millimeters. b. Convert 10.0 meters to kilometers. c. Convert 550.0 kilograms to grams. d. Convert 150.5 milligrams to grams. e. Convert 0.500 liters to milliliters. f. Convert 250.0 ml to liters.
The Correct Answer and Explanation is:
1. Convert 1760 yards to miles
1 mile = 1760 yards
1760 yards × (1 mile / 1760 yards) = 1.00 mile (3 significant figures)
2. Convert 1.289 × 10⁷ miles to meters
1 mile = 1609.34 meters
1.289 × 10⁷ miles × 1609.34 m/mile = 2.073 × 10¹⁰ meters (4 significant figures)
3. Convert 850 kilocalories to kilojoules
1 kilocalorie = 4.184 kilojoules
850 kcal × 4.184 kJ/kcal = 3556 kJ (3 significant figures)
4. Convert 125 inches to millimeters
1 inch = 25.4 mm
125 in × 25.4 mm/in = 3175 mm (3 significant figures)
5. Convert 828.5 pounds to kilograms
1 pound = 0.453592 kg
828.5 lb × 0.453592 kg/lb = 375.8 kg (4 significant figures)
6. Density Calculations:
a. 100.0 grams / 900.0 ml = 0.1111 g/ml (4 significant figures)
b. Volume = mass / density = 79.1 g / 0.790 g/ml = 100.1 ml = 0.1001 L (4 significant figures)
7. Metric to Metric Conversions:
a. 10.0 meters × 1000 mm/m = 1.00 × 10⁴ mm (3 significant figures)
b. 10.0 meters × (1 km / 1000 m) = 0.0100 km (3 significant figures)
c. 550.0 kg × 1000 g/kg = 5.500 × 10⁵ g (4 significant figures)
d. 150.5 mg × (1 g / 1000 mg) = 0.1505 g (4 significant figures)
e. 0.500 liters × 1000 ml/L = 500. ml (3 significant figures)
f. 250.0 ml × (1 L / 1000 ml) = 0.2500 L (4 significant figures)
Explanation
Unit conversions are fundamental in science to ensure consistency and clarity. Each answer above is calculated using precise conversion factors, and the number of significant figures in the result matches the precision of the given data.
In the first problem, 1760 yards exactly equals 1 mile by definition. It has three significant figures, so the answer does as well. The conversion from miles to meters uses the standard factor of 1609.34 meters per mile, and the result maintains four significant figures based on the original number.
When converting energy from kilocalories to kilojoules, the factor 4.184 is exact. The result respects the three significant figures of the original value. The same principle applies when converting inches to millimeters using 25.4 mm per inch.
Weight conversion from pounds to kilograms uses the factor 0.453592, and the result has four significant digits because the given value does. Density calculations use the formula density = mass/volume. When dividing two quantities with four significant figures, the result also retains four.
In the second density-related calculation, the volume is derived from the given mass and density. The result in milliliters is then converted to liters by dividing by 1000.
Metric to metric conversions are often simpler because they involve powers of 10. Multiplying or dividing by 10, 100, or 1000 ensures that units are converted properly while still preserving the correct number of significant figures.
Overall, attention to significant figures reflects the precision of measurements and avoids implying accuracy that does not exist in the original data.
