Questions and Answers
How many significant figures are in the number 39,004?
What is the significance of leading zeros in a number?
Which of these numbers has three significant figures?
How should trailing zeros in a decimal number be treated?
Signup and view all the answers
What is the total number of significant figures in the scientific notation 1.400 × 10^3?
Signup and view all the answers
Which statement about the number 0.008 is correct?
Signup and view all the answers
In the number 620.0, how many significant figures are present?
Signup and view all the answers
Which of the following is a correct example of scientific notation for the number with four significant figures?
Signup and view all the answers
What is the correct rounded answer for the addition problem $180.156 + 342.4$?
Signup and view all the answers
When calculating density using the mass 37.46 g and volume 12.7 cm³, what is the resultant density rounded to the correct number of significant figures?
Signup and view all the answers
Which statement correctly explains how to round answers in multiplication and division?
Signup and view all the answers
What is the scientific notation of the number 0.022?
Signup and view all the answers
If the mass of an object is given as 50.0 g and the volume is 20.0 cm³, what is the density rounded to the correct significant figures?
Signup and view all the answers
In the context of significant figures, how many significant figures are in the number 7128.6?
Signup and view all the answers
Which of the following numbers has 3 significant figures?
Signup and view all the answers
What is the proper rounding of the result from dividing 100 by 3.456, where 100 has only 1 significant figure?
Signup and view all the answers
Study Notes
Rules for Significant Figures
- All nonzero digits in a measurement are significant.
- Middle zeros, which appear between nonzero digits, are always significant.
- Leading zeros, which precede all nonzero digits, are not significant.
- Trailing zeros, which follow all nonzero digits, may be ambiguous without a decimal point; use scientific notation for clarity.
- Trailing zeros in a number with a decimal point are significant, regardless of their position relative to the decimal point.
Examples of Significant Figures
- 237 contains three significant figures.
- 1.897 contains four significant figures.
- 39,004 has five significant figures.
- 0.008 has one significant figure due to leading zeros.
- 1400 is ambiguous without clarification on trailing zeros.
- Scientific notation clarifies significant figures, e.g., 1.40 × 10^3 indicates three significant figures.
Rules for Mathematical Operations
-
For addition and subtraction, round the answer to the same number of decimal places as the measurement with the least decimal places.
-
Example: 180.156 + 342.4 = 522.456 rounds to 522.5 g/mol.
-
For multiplication and division, the result is rounded to the same number of significant figures as the measurement with the least significant figures.
-
Example: The calculation ( 37.46 \text{ g} \div 12.7 \text{ cm}^3 = 2.949606299 \text{ g/cm}^3 ) rounds to 2.95 g/cm³.
Converting Standard Notation to Scientific Notation
- Determine significant figures in the measurement.
- Example: 7128.6 mL equals five significant figures; 0.022 m equals two significant figures.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on the rules of significant figures with this engaging quiz. Explore different examples and learn how to accurately measure significant digits in various numbers. Perfect for students in math and science classes.
