Q1. Express each number in scientific notation:

Background

Topic: Scientific Notation

This question tests your ability to convert standard decimal numbers into scientific notation, which is a way of expressing very large or very small numbers using powers of ten.

Key Terms:

• Scientific notation: A number written as , where and is an integer.

Step-by-Step Guidance

1. For each number, identify how many places the decimal point must move to create a number between 1 and 10.

2. Count the number of decimal places moved; this determines the exponent .

3. If the decimal moves to the right (for small numbers), is negative; if to the left (for large numbers), is positive.

4. Write the number as .

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Q2. How many significant figures are in each of the following numbers?

Background

Topic: Significant Figures

This question tests your understanding of how to count significant digits in a number, which is important for reporting measurements accurately.

Key Terms:

• Significant figures: Digits in a number that are meaningful in terms of accuracy.

• Rules: All nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros in a decimal are significant.

Step-by-Step Guidance

1. For each number, apply the rules for significant figures.

2. Count all nonzero digits and zeros that are significant according to their position.

3. For numbers in scientific notation, only the digits in the coefficient are counted.

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Q3. Carry out the following operations, and express the answers with the appropriate number of significant figures:

Background

Topic: Significant Figures in Calculations

This question tests your ability to perform arithmetic operations and report the result with the correct number of significant figures.

Key Terms and Formulas:

• Addition/Subtraction: The answer should have the same number of decimal places as the measurement with the fewest decimal places.

• Multiplication/Division: The answer should have the same number of significant figures as the measurement with the fewest significant figures.

Step-by-Step Guidance

1. Perform the calculation for each operation.

2. For addition/subtraction, check the decimal places in each number and round the result accordingly.

3. For multiplication/division, count the significant figures in each number and round the result to match the lowest count.

4. Write the answer with the correct number of significant figures.

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Q4. Report the correct answer (with proper significant figures) for each calculation:

Background

Topic: Significant Figures in Multi-Step Calculations

This question tests your ability to apply significant figure rules to multi-step calculations and select the correct answer from multiple choices.

Key Terms and Formulas:

• For multiplication/division, use the lowest number of significant figures in the calculation.

• For addition/subtraction, use the lowest number of decimal places.

Step-by-Step Guidance

1. Perform the calculation step by step, keeping track of significant figures at each stage.

2. For each operation, apply the appropriate rule for significant figures.

3. After completing the calculation, round the result to the correct number of significant figures.

4. Compare your rounded result to the answer choices provided.

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Q5. Which measurement below represents the heaviest mass?

Background

Topic: SI Units and Prefixes

This question tests your understanding of SI unit prefixes and their relative sizes.

Key Terms:

• SI prefixes: kilo (k), mega (M), deci (d), milli (m), pico (p), etc.

• 1 kg = g; 1 Mg = g; 1 dg = g; 1 mg = g; 1 pg = g

Step-by-Step Guidance

1. Convert each mass to grams using the appropriate prefix.

2. Compare the values to determine which is largest.

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Q6. The correct prefix for the multiplier 1000 is:

Background

Topic: SI Prefixes

This question tests your knowledge of SI prefixes and their corresponding multipliers.

Key Terms:

• kilo (k):

• micro ():

• nano (n):

• milli (m):

• mega (M):

Step-by-Step Guidance

1. Recall the SI prefix for .

2. Compare the options to the correct prefix.

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Q7. a) What is the standard SI unit for length?

Background

Topic: SI Units

This question tests your knowledge of the standard SI units for fundamental measurements.

Key Terms:

• SI unit for length: meter (m)

Step-by-Step Guidance

1. Recall the SI unit for length.

2. Identify the correct option from the list.

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Q7. b) The standard SI unit for temperature is:

Background

Topic: SI Units

This question tests your knowledge of the SI unit for temperature.

Key Terms:

• SI unit for temperature: Kelvin (K)

Step-by-Step Guidance

1. Recall the SI unit for temperature.

2. Identify the correct option from the list.

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Q8. Perform the following conversions:

Background

Topic: Unit Conversions

This question tests your ability to convert between units using conversion factors.

Key Terms and Formulas:

• Conversion factor: A ratio used to convert from one unit to another.

• Common conversions: , , , ,

Step-by-Step Guidance

1. For each conversion, write the starting value and the conversion factor.

2. Set up the calculation so that units cancel appropriately.

3. Multiply or divide as needed to obtain the desired unit.

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Q9. a) The speed of light in a vacuum is m/s. Calculate its speed in km/hr.

Background

Topic: Unit Conversions (Speed)

This question tests your ability to convert speed from meters per second to kilometers per hour.

Key Terms and Formulas:

Step-by-Step Guidance

1. Write the speed in m/s.

2. Multiply by the conversion factor to change meters to kilometers.

3. Multiply by the conversion factor to change seconds to hours.

4. Set up the calculation so that units cancel and you are left with km/hr.

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Q9. b) The Sears Tower in Chicago is 1454 ft. tall. Calculate its height in meters.

Background

Topic: Unit Conversions (Length)

This question tests your ability to convert feet to meters using intermediate conversions.

Key Terms and Formulas:

Step-by-Step Guidance

1. Write the height in feet.

2. Convert feet to inches.

3. Convert inches to centimeters.

4. Convert centimeters to meters.

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Q9. c) Convert 0.420 in/ms to km/hr

Background

Topic: Unit Conversions (Speed)

This question tests your ability to convert a speed from inches per millisecond to kilometers per hour.

Key Terms and Formulas:

Step-by-Step Guidance

1. Write the speed in in/ms.

2. Convert inches to centimeters, then to meters, then to kilometers.

3. Convert milliseconds to seconds, then to hours.

4. Set up the calculation so that units cancel and you are left with km/hr.

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Q10. How many microliters are in 41.0 mL?

Background

Topic: Unit Conversions (Volume)

This question tests your ability to convert milliliters to microliters using SI prefixes.

Key Terms and Formulas:

Step-by-Step Guidance

1. Write the volume in mL.

2. Multiply by the conversion factor to change mL to L.

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Q11. A sample of an unknown metal has a mass of 35.4 g and a volume of 3.11 cm3. Calculate its density. Identify the metal by comparison to Table in the textbook.

Background

Topic: Density

This question tests your ability to calculate density and use it to identify a substance.

Key Terms and Formulas:

• Density formula:

Step-by-Step Guidance

1. Write the mass and volume values.

2. Plug the values into the density formula.

3. Calculate the density, keeping units in g/cm3.

4. Compare the calculated density to known values in your textbook to identify the metal.

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Q12. Glycerol is a syrupy liquid often used in cosmetics and soaps. A 2.50-L sample of pure glycerol has a mass of g. What is the density of glycerol in grams per cubic centimeter?

Background

Topic: Density and Unit Conversion

This question tests your ability to calculate density and convert units from liters to cubic centimeters.

Key Terms and Formulas:

• Density formula:

Step-by-Step Guidance

1. Write the mass and volume values.

2. Convert the volume from liters to cubic centimeters.

3. Plug the values into the density formula.

4. Calculate the density in g/cm3.

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Q13. a) Acetone (fingernail-polish remover) has a density of 0.7857 g/cm3. What is the mass in grams of 17.53 mL of acetone?

Background

Topic: Density and Mass Calculation

This question tests your ability to use density to find mass from volume.

Key Terms and Formulas:

• Density formula:

Step-by-Step Guidance

1. Write the density and volume values.

2. Use the formula .

3. Plug in the values and calculate the mass.

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Q13. b) What is the volume in milliliters of 7.24 g of acetone?

Background

Topic: Density and Volume Calculation

This question tests your ability to use density to find volume from mass.

Key Terms and Formulas:

• Density formula:

• Rearranged:

Step-by-Step Guidance

1. Write the mass and density values.

2. Use the formula .

3. Plug in the values and calculate the volume.

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Q14. How many liters of air are in a room that measures 10.0 ft × 11.0 ft and has an 8.00 ft ceiling?

Background

Topic: Volume and Unit Conversions

This question tests your ability to calculate the volume of a room and convert units from cubic feet to liters.

Key Terms and Formulas:

• Volume formula:

Step-by-Step Guidance

1. Calculate the volume in cubic feet by multiplying the three dimensions.

2. Convert cubic feet to cubic inches, then to cubic centimeters.

3. Convert cubic centimeters to milliliters, then to liters.

4. Set up the calculation so that units cancel and you are left with liters.

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