Significant Figures Questions And Answers Pdf

Significant Figures: Questions and Answers

Understanding significant figures is crucial for anyone working with numerical data, especially in scientific fields. It's a fundamental concept that dictates the precision and accuracy of measurements and calculations. This comprehensive guide delves into significant figures, providing a wealth of questions and answers to solidify your understanding. We'll cover everything from basic rules to more complex scenarios involving calculations and scientific notation. Downloading a PDF might be helpful for offline reference, but this article aims to be your complete, self-contained guide.

What are Significant Figures (Sig Figs)?

Significant figures, also known as sig figs, represent the digits in a number that carry meaning contributing to its measurement resolution. They reflect the precision of a measurement. Non-zero digits are always significant. The rules for determining significant figures are as follows:

Rules for Determining Significant Figures:

1. Non-zero digits: All non-zero digits are significant. For example, in the number 234, all three digits are significant.

2. Zeros:

   • Leading zeros: Zeros before the first non-zero digit are not significant. For example, in 0.00234, only 2, 3, and 4 are significant.
   • Trailing zeros: Trailing zeros (zeros at the end of a number) are significant only if the number contains a decimal point. For example:
     • 2340 has three significant figures.
     • 2340. has four significant figures.
     • 2340.0 has five significant figures.
   • Captive zeros: Zeros between non-zero digits are significant. For example, in 2003, all four digits are significant.

3. Scientific Notation: In scientific notation (e.g., 2.34 x 10³), all digits in the coefficient are significant.

Significant Figures: Practice Questions and Answers

Let's test your understanding with some examples. Remember to apply the rules carefully!

Question 1: How many significant figures are in the number 1200?

Answer 1: Two. The trailing zeros are not significant because there's no decimal point.

Question 2: How many significant figures are in 0.00450?

Answer 2: Three. The leading zeros are not significant, but the trailing zero is because of the decimal point.

Question 3: How many significant figures are in 300.0?

Answer 3: Four. All digits, including the trailing zeros after the decimal point, are significant.

Question 4: How many significant figures are in 1.02 x 10⁴?

Answer 4: Three. Only the digits in the coefficient (1.02) are considered.

Question 5: How many significant figures are in 90000?

Answer 5: One. In this form, it is difficult to know the intention of the number. It only contains a single significant digit; the trailing zeros are not significant without a decimal point. To show more significance, we would use scientific notation like 9.00 x 10⁴ (3 sig figs) or 9.0000 x 10⁴ (5 sig figs).

Question 6: What is the result of 3.456 + 12.3 + 0.001, expressed with the correct number of significant figures?

Answer 6: 15.8. When adding or subtracting, the result should have the same number of decimal places as the measurement with the fewest decimal places. In this case, 12.3 has only one decimal place, so the answer is rounded to one decimal place.

Question 7: What is the result of 12.4 x 3.2 expressed with the correct number of significant figures?

Answer 7: 39.7 (or 40 depending on rounding rules). When multiplying or dividing, the answer should have the same number of significant figures as the measurement with the fewest significant figures. Both 12.4 and 3.2 have three significant figures, so the answer should also have three significant figures. Depending on rounding rules, you might round to 40 if only two significant figures are to be shown.

Question 8: Calculate 5.234 / 0.0021 to the correct number of significant figures.

Answer 8: 2492 (or 2500). Since 0.0021 has two significant figures, the final answer should also have two significant figures. Rounding based on rules for the most significant digit, this becomes 2500 (or possibly 2490 depending on rounding rules).

Advanced Significant Figures Questions and Answers

Now let's tackle some more challenging problems that involve combined operations and scientific notation.

Question 9: (1.23 x 10²) + (4.56 x 10¹) = ? (with correct significant figures)

Answer 9: To add numbers in scientific notation, you must first ensure they have the same exponent. Then add the coefficients, and express the result with the correct number of significant figures. This is best done by standard addition.

1.23 x 10² + 0.456 x 10² = 1.686 x 10² This rounds to 1.69 x 10²

Question 10: (6.78 x 10⁻³) x (2.3 x 10⁴) = ? (with correct significant figures)

Answer 10: For multiplication, multiply the coefficients and add the exponents. The result is 15.6 x 10¹, which in proper scientific notation is 1.6 x 10². (Note: 2.3 has two significant figures, dictating the final answer.)

Question 11: A rectangular block has dimensions 2.5 cm, 4.75 cm, and 10.0 cm. What is its volume, with the correct number of significant figures?

Answer 11: The volume is calculated by multiplying the three dimensions. 2.5 cm * 4.75 cm * 10.0 cm = 118.75 cm³. The value 2.5 has two significant figures, so the answer should be rounded to two significant figures: 120 cm³.

Question 12: A student measures the mass of an object to be 10.2 g and its volume to be 2.5 mL. Calculate the density (density = mass/volume) with the correct number of significant figures.

Answer 12: Density = 10.2 g / 2.5 mL = 4.08 g/mL. Since 2.5 has two significant figures, the final answer should also have two significant figures: 4.1 g/mL.

Rounding Rules for Significant Figures

When rounding, follow these rules:

• If the digit to be dropped is less than 5, the preceding digit remains unchanged.
• If the digit to be dropped is 5 or greater, the preceding digit is increased by 1.

Why are Significant Figures Important?

Understanding significant figures is essential because it prevents the propagation of errors and misrepresentation of the accuracy of measurements and calculations. Reporting a result with excessive significant figures implies a level of precision that wasn't actually achieved. Similarly, using too few significant figures can lead to a loss of valuable information. Maintaining appropriate significant figures in scientific calculations allows clear communication of data uncertainty and accuracy.

This detailed guide and practice questions provide a solid foundation in significant figures. While a PDF may offer a convenient format, remember that understanding the underlying principles and applying the rules correctly is key to mastering this fundamental concept. Consistent practice is essential for developing proficiency in working with significant figures and ensuring accuracy in scientific and technical calculations. Remember to always double-check your work and consider the context of your calculations.