Math Problem Statement

Answer the following: (Show your computation and round off the final answer to 2 decimal places)

  1. A man makes a 27.0-kilometer trip in 16 minutes. How many miles did he travel?

  2. The density of propane is 36.28 lb/ft3. Convert this to kg/m3.

  3. How many significant figures are there in 685.602?

  4. A length of glass tubing is 0.525 meter. How many inches long is the tubing?

  5. What is the density in g/mL of a sample mineral oil if it has 250 milliliter and has a mass of 0.23 kilogram?

  6. If the density of carbon tetrachloride is 0.793 g/mL, and a sample has a volume of 9.29 milliliter, what is the mass?

  7. What is the density in g/mL of a substance that has mass of 0.987 kg and has a volume of 4.52 x 102 milliliter?

  8. How many kilometers are there in 2.88 meter?

  9. How many pounds does 2.00 kilogram of cheese weighs?

  10. How many degrees Fahrenheit are there in 30.0 °C?

Solution

Here are the solutions with computations:

1. Convert kilometers to miles

1 km=0.621371 miles1 \text{ km} = 0.621371 \text{ miles} 27.0×0.621371=16.77699927.0 \times 0.621371 = 16.776999 Final Answer: 16.78 miles


2. Convert density of propane to kg/m³

1 lb=0.453592 kg,1 ft3=0.0283168 m31 \text{ lb} = 0.453592 \text{ kg}, \quad 1 \text{ ft}^3 = 0.0283168 \text{ m}^3 36.28×0.4535920.0283168\frac{36.28 \times 0.453592}{0.0283168} =16.4550.0283168=581.3= \frac{16.455}{0.0283168} = 581.3 Final Answer: 581.30 kg/m³


3. Significant Figures in 685.602

  • All nonzero digits are significant.
  • Any zeros between significant figures are counted.
  • Trailing zeros after a decimal point are significant.
    Answer: 6 significant figures

4. Convert meters to inches

1 m=39.3701 inches1 \text{ m} = 39.3701 \text{ inches} 0.525×39.3701=20.66930.525 \times 39.3701 = 20.6693 Final Answer: 20.67 inches


5. Density in g/mL

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}} 0.23 kg×1000 g/kg250 mL\frac{0.23 \text{ kg} \times 1000 \text{ g/kg}}{250 \text{ mL}} =230250=0.92= \frac{230}{250} = 0.92 Final Answer: 0.92 g/mL


6. Mass of Carbon Tetrachloride Sample

Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume} 0.793×9.29=7.369970.793 \times 9.29 = 7.36997 Final Answer: 7.37 g


7. Density of a Substance in g/mL

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}} 0.987×10004.52×102\frac{0.987 \times 1000}{4.52 \times 10^2} =987452=2.18= \frac{987}{452} = 2.18 Final Answer: 2.18 g/mL


8. Convert meters to kilometers

1 m=0.001 km1 \text{ m} = 0.001 \text{ km} 2.88×0.001=0.002882.88 \times 0.001 = 0.00288 Final Answer: 0.00288 km


9. Convert kilograms to pounds

1 kg=2.20462 lb1 \text{ kg} = 2.20462 \text{ lb} 2.00×2.20462=4.409242.00 \times 2.20462 = 4.40924 Final Answer: 4.41 lb


10. Convert Celsius to Fahrenheit

F=95C+32F = \frac{9}{5}C + 32 =95(30.0)+32= \frac{9}{5} (30.0) + 32 =54+32=86= 54 + 32 = 86 Final Answer: 86.00°F


Would you like further clarifications? Here are five related questions to deepen understanding:

  1. How do significant figures affect the precision of calculations?
  2. Why do different materials have different densities?
  3. What is the relationship between mass, volume, and density?
  4. How do you convert between different temperature scales (Kelvin, Celsius, Fahrenheit)?
  5. Why is unit conversion important in scientific measurements?

Tip: Always check unit consistency when performing conversions to avoid miscalculations. 🚀

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Density Calculation
Significant Figures
Temperature Conversion

Formulas

1 km = 0.621371 miles
1 lb = 0.453592 kg
1 ft^3 = 0.0283168 m^3
Density = Mass / Volume
1 m = 39.3701 inches
1 kg = 2.20462 lb
Fahrenheit = (9/5) * Celsius + 32

Theorems

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Suitable Grade Level

Grades 9-12