Dimensional Analysis and Unit Conversion Practice Guidance

Q1. (8.881 x 2.100) + 0.590 = ?

Background

Topic: Significant Figures and Order of Operations

This question tests your ability to perform calculations with correct significant figures, including multiplication and addition.

Key Terms and Formulas:

• Significant Figures: The number of meaningful digits in a measured or calculated quantity.

• Order of Operations: Perform multiplication before addition.

Step-by-Step Guidance

1. First, multiply 8.881 by 2.100. Pay attention to the number of significant figures in each value.

2. Determine the correct number of significant figures for the result of the multiplication (the answer should have as many significant figures as the value with the fewest significant figures).

3. Next, add the result of the multiplication to 0.590. When adding, the answer should be rounded to the least number of decimal places present in the numbers being added.

4. Set up the final expression, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q2. (922 + 89.6) / 4.100 = ?

Background

Topic: Significant Figures in Addition and Division

This question tests your ability to apply significant figure rules in both addition and division.

Key Terms and Formulas:

• Significant Figures: Rules differ for addition/subtraction (least decimal places) and multiplication/division (least significant figures).

Step-by-Step Guidance

1. Add 922 and 89.6. For addition, round the result to the least number of decimal places in the numbers being added.

2. Divide the sum by 4.100. For division, the result should have as many significant figures as the value with the fewest significant figures.

3. Set up the final division, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q3. How many mm3 are in 16.7 cm3?

Background

Topic: Volume Unit Conversion

This question tests your ability to convert between cubic centimeters and cubic millimeters.

Key Terms and Formulas:

• 1 cm = 10 mm

• 1 cm3 = (10 mm)3 = 1000 mm3

Step-by-Step Guidance

1. Write the given volume: 16.7 cm3.

2. Set up the conversion factor: $1 \ \text{cm}^3 = 1000 \ \text{mm}^3$.

3. Multiply the given value by the conversion factor to convert to mm3.

4. Set up the multiplication, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q4. What is the value of a diffusion coefficient of 18.5 in2/min expressed in cm2/s? (2.54 cm = 1 in)

Background

Topic: Unit Conversion (Area and Time)

This question tests your ability to convert both area units (in2 to cm2) and time units (min to s).

Key Terms and Formulas:

• 1 in = 2.54 cm

• 1 in2 = (2.54 cm)2

• 1 min = 60 s

Step-by-Step Guidance

1. Start with the given value: 18.5 in2/min.

2. Convert in2 to cm2 using $1 \ \text{in}^2 = (2.54)^2 \ \text{cm}^2$.

3. Convert min to s using $1 \ \text{min} = 60 \ \text{s}$.

4. Set up the conversion as a chain of fractions, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q5. If a car has an EPA mileage rating of 26.0 miles per gallon, what is this rating in kilometers per liter? Helpful conversions: 1 L = 1.06 qt; 1 mile = 1.609 km; 4 qt = 1 gallon

Background

Topic: Multi-Step Unit Conversion (Distance and Volume)

This question tests your ability to convert both distance (miles to kilometers) and volume (gallons to liters).

Key Terms and Formulas:

• 1 mile = 1.609 km

• 4 qt = 1 gallon

• 1 L = 1.06 qt

Step-by-Step Guidance

1. Start with the given value: 26.0 miles/gallon.

2. Convert miles to kilometers using $1 \ \text{mile} = 1.609 \ \text{km}$.

3. Convert gallons to quarts, then quarts to liters using the provided conversion factors.

4. Set up the chain of conversions so that miles and gallons cancel, leaving km/L.

5. Do not compute the final value yet.

Try solving on your own before revealing the answer!

Q6. A 15.423 mL urine sample has a mass of 2.74 g. Its specific gravity is?

Background

Topic: Specific Gravity Calculation

This question tests your ability to calculate specific gravity, which is the ratio of the density of a substance to the density of water.

Key Terms and Formulas:

• Specific Gravity = (Density of sample) / (Density of water)

• Density = mass / volume

• Density of water at room temperature ≈ 1.00 g/mL

Step-by-Step Guidance

1. Calculate the density of the urine sample using $\text{Density} = \frac{\text{mass}}{\text{volume}}$.

2. Divide the calculated density by the density of water to find the specific gravity.

3. Set up the final expression, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q7. How many pounds are in 3.5 kg? [1 lb. = 453.59 g]

Background

Topic: Mass Unit Conversion

This question tests your ability to convert between kilograms and pounds using a two-step conversion (kg to g, then g to lb).

Key Terms and Formulas:

• 1 kg = 1000 g

• 1 lb = 453.59 g

Step-by-Step Guidance

1. Convert 3.5 kg to grams using $1 \ \text{kg} = 1000 \ \text{g}$.

2. Convert grams to pounds using $1 \ \text{lb} = 453.59 \ \text{g}$.

3. Set up the chain of conversions, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q8. The density of gold (Au) is 19.3 g/mL. Determine the mass in kilograms of Au that will occupy 950. mL of space.

Background

Topic: Density and Mass Calculation

This question tests your ability to use density to find mass, and then convert the mass to kilograms.

Key Terms and Formulas:

• Density = mass / volume

• Rearranged: mass = density × volume

• 1 kg = 1000 g

Step-by-Step Guidance

1. Calculate the mass in grams using $\text{mass} = \text{density} \times \text{volume}$.

2. Convert the mass from grams to kilograms using $1 \ \text{kg} = 1000 \ \text{g}$.

3. Set up the final conversion, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q9. Complete the following conversions:

• 612 g = ? mg

• 8.160 = ? cm

• 3779 µg = ? g

• 781 mL = ? L

• 4.18 kg = ? g

• 27.8 m = ? km

• 0.13 mL = ? L

• 1738 km = ? m

• 1.9 Gg = ? g

Background

Topic: Metric Unit Conversions

This question tests your ability to convert between different metric units using powers of ten.

Key Terms and Formulas:

• 1 g = 1000 mg

• 1 µg = 1 × 10-6 g

• 1 mL = 0.001 L

• 1 kg = 1000 g

• 1 m = 0.001 km

• 1 km = 1000 m

• 1 Gg = 1 × 109 g

Step-by-Step Guidance

1. For each conversion, write the given value and the appropriate conversion factor.

2. Set up the conversion as a multiplication or division, making sure units cancel appropriately.

3. Do not compute the final values yet; just set up the expressions for each.

Try solving on your own before revealing the answer!