Skip to main content
Back

Significant Figures, Scientific Notation, and Calculations – Step-by-Step Guidance

NotesPracticeVideo lessons

Study Guide - Smart Notes

Tailored notes based on your materials, expanded with key definitions, examples, and context.

Q2. How many significant figures does the number 46.000 contain?

Background

Topic: Significant Figures

This question tests your understanding of how to count significant figures in a number, especially when zeros are present after the decimal point.

Key Terms:

  • Significant Figures: The digits in a number that carry meaning contributing to its precision.

  • Trailing Zeros: Zeros at the end of a number; they are significant if there is a decimal point present.

Step-by-Step Guidance

  1. Identify all nonzero digits in the number 46.000. These are always significant.

  2. Look at the zeros after the decimal point. Are they considered significant? (Recall: Trailing zeros after a decimal point are significant.)

  3. Count all the significant digits, including both nonzero digits and any zeros that are significant.

Try solving on your own before revealing the answer!

Q3. Convert the following to standard (regular) notation: 6.15 × 10^4

Background

Topic: Scientific Notation

This question tests your ability to convert a number from scientific notation to standard decimal notation.

Key Terms and Formula:

  • Scientific Notation: A way of expressing numbers as a product of a coefficient and a power of ten.

  • Standard Notation: The usual way of writing numbers without exponents.

Step-by-Step Guidance

  1. Identify the coefficient (6.15) and the exponent (4) in the scientific notation.

  2. Since the exponent is positive, move the decimal point to the right by the number of places equal to the exponent.

  3. Write out the number in standard notation, making sure to add zeros if needed.

Try solving on your own before revealing the answer!

Q4. What is the correct answer to this calculation, rounded to the correct number of significant figures? 0.0954 × 2083 / 5.034

Background

Topic: Significant Figures in Calculations

This question tests your ability to perform multiplication and division while keeping track of significant figures.

Key Terms and Formula:

  • Multiplication/Division 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 value: 0.0954, 2083, and 5.034.

  2. Perform the calculation: multiply 0.0954 by 2083, then divide by 5.034.

  3. Determine which value has the fewest significant figures. This will dictate how many significant figures your final answer should have.

  4. Round your answer to match the correct number of significant figures.

Try solving on your own before revealing the answer!

Q5. How many significant figures does the number 2.10 × 10−3 contain?

Background

Topic: Significant Figures

This question tests your ability to count significant figures in a number written in scientific notation.

Key Terms:

  • Scientific Notation: Only the digits in the coefficient (before the ×10) are considered for significant figures.

Step-by-Step Guidance

  1. Look at the coefficient (2.10) and ignore the exponent part for significant figures.

  2. Count all nonzero digits and any zeros between or after nonzero digits in the coefficient.

Try solving on your own before revealing the answer!

Q7. How many significant figures does the number 0.0011 contain?

Background

Topic: Significant Figures

This question tests your ability to identify significant figures in a number with leading zeros.

Key Terms:

  • Leading Zeros: Zeros before the first nonzero digit are not significant.

Step-by-Step Guidance

  1. Identify and ignore all leading zeros (those before the first nonzero digit).

  2. Count the remaining digits, which are significant.

Try solving on your own before revealing the answer!

Q9. Perform the following calculation to the correct number of significant figures: 41.024 + 3.5 / 42.11

Background

Topic: Significant Figures in Addition and Division

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

Key Terms and Formulas:

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

  • Division Rule: The result should have as many significant figures as the value with the fewest significant figures.

Step-by-Step Guidance

  1. First, perform the addition: 41.024 + 3.5. Apply the addition rule for significant figures (focus on decimal places).

  2. Next, divide the sum by 42.11. Apply the division rule for significant figures (focus on total significant figures).

  3. Round your answer to the correct number of significant figures based on the rules above.

Try solving on your own before revealing the answer!

Q10. How many significant figures does the number 308 contain?

Background

Topic: Significant Figures

This question tests your ability to count significant figures in a whole number without a decimal point.

Key Terms:

  • Captive Zeros: Zeros between nonzero digits are always significant.

Step-by-Step Guidance

  1. Identify all nonzero digits in the number.

  2. Determine if any zeros are between nonzero digits (captive zeros) and count them as significant.

  3. Count the total number of significant digits.

Try solving on your own before revealing the answer!

Q11. What is the correct answer to this calculation, rounded to the correct number of significant figures? 16.01 × (366.1 / 381)

Background

Topic: Significant Figures in Multiplication and Division

This question tests your ability to apply significant figure rules in a calculation involving both multiplication and division.

Key Terms and Formula:

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

Step-by-Step Guidance

  1. First, perform the division inside the parentheses: 366.1 / 381. Determine the number of significant figures for each value.

  2. Next, multiply the result by 16.01. Again, consider the number of significant figures in each value.

  3. Round your final answer to the correct number of significant figures based on the value with the fewest significant figures.

Try solving on your own before revealing the answer!

Q12. How many significant figures does the number 3468 contain?

Background

Topic: Significant Figures

This question tests your ability to count significant figures in a whole number with no decimal point.

Key Terms:

  • Nonzero digits: Always significant.

  • Zeros: Only significant if between nonzero digits or after a decimal point.

Step-by-Step Guidance

  1. Identify all nonzero digits in the number.

  2. Check for any zeros and determine if they are significant based on their position.

  3. Count the total number of significant digits.

Try solving on your own before revealing the answer!

Q13. Which of the following numbers is the largest?

Background

Topic: Comparing Numbers in Scientific Notation

This question tests your ability to compare numbers written in scientific notation and standard notation.

Key Terms:

  • Scientific Notation: Expresses numbers as a coefficient times a power of ten.

  • Standard Notation: The usual way of writing numbers.

Step-by-Step Guidance

  1. Convert each number to standard notation if needed.

  2. Compare the values to determine which is the largest.

Try solving on your own before revealing the answer!

Pearson Logo

Study Prep