Q1. Perform the following calculation and give the answer with the correct number of significant figures: 32.5 × 0.019

Background

Topic: Significant Figures in Multiplication

This question tests your ability to multiply numbers and report the answer with the correct number of significant figures.

Key Terms and Formulas

• Significant Figures: The digits in a measurement that are known with certainty plus one estimated digit.

• Multiplication Rule: The result should have as many significant figures as the measurement with the fewest significant figures.

Step-by-Step Guidance

1. Identify the number of significant figures in each number: 32.5 (3 sig figs), 0.019 (2 sig figs).

2. Multiply the two numbers:

3. Determine how many significant figures your answer should have (use the smaller number of sig figs from the original numbers).

4. Set up your answer to be rounded to the correct number of significant figures.

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Q2. Perform the following calculation and give the answer with the correct number of significant figures: 2.40 + 31

Background

Topic: Significant Figures in Addition

This question tests your ability to add numbers and report the answer with the correct number of decimal places.

Key Terms and Formulas

• Addition Rule: The result should have the same number of decimal places as the measurement with the fewest decimal places.

Step-by-Step Guidance

1. Identify the number of decimal places in each number: 2.40 (2 decimal places), 31 (0 decimal places).

2. Add the two numbers:

3. Determine how many decimal places your answer should have (use the smallest number of decimal places from the original numbers).

4. Set up your answer to be rounded to the correct number of decimal places.

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Q3. Perform the following calculation and give the answer with the correct number of significant figures: 2.1 × 0.059

Background

Topic: Significant Figures in Multiplication

This question tests your ability to multiply numbers and report the answer with the correct number of significant figures.

Key Terms and Formulas

• Multiplication Rule: The result should have as many significant figures as the measurement with the fewest significant figures.

Step-by-Step Guidance

1. Count the significant figures in each number: 2.1 (2 sig figs), 0.059 (2 sig figs).

2. Multiply the numbers:

3. Determine the correct number of significant figures for your answer.

4. Set up your answer to be rounded to the correct number of significant figures.

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Q4. Which one of the following correctly pairs the prefix with its abbreviation?

Background

Topic: SI Prefixes

This question tests your knowledge of the correct abbreviations for metric prefixes.

Key Terms

• Giga- (G):

• Tera- (T):

• Peta- (P):

Step-by-Step Guidance

1. Recall the standard SI prefixes and their abbreviations.

2. Match the given prefix to its correct abbreviation.

3. Check for common mistakes (e.g., confusing Giga- with G or M).

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Q5. Using the table of equalities, select the correct conversion factors that indicate the number of feet (ft) in one mile (mi).

Background

Topic: Unit Conversions

This question tests your ability to use conversion factors to relate different units of length.

Key Terms and Formulas

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

• Common Length Conversion:

Step-by-Step Guidance

1. Locate the conversion factor for miles to feet in the provided table.

2. Write the conversion as a ratio: or depending on the direction of conversion.

3. Ensure you understand which unit is in the numerator and which is in the denominator for your calculation.

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Q6. Rank the following lengths in order of increasing size (smallest to largest): 1 picometer, 1 nanometer, 1 millimeter, 1 decimeter

Background

Topic: Metric Prefixes and Relative Sizes

This question tests your understanding of the relative sizes of metric units.

Key Terms

• picometer (pm): m

• nanometer (nm): m

• millimeter (mm): m

• decimeter (dm): m

Step-by-Step Guidance

1. Write each unit in terms of meters using scientific notation.

2. Compare the exponents to determine which is smallest and which is largest.

3. Arrange the units from smallest to largest based on their values in meters.

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