Type The Correct Answer In Each Box.Solve The Problems. Express Your Answers To The Correct Number Of Significant Figures.$\[ \begin{array}{l} \frac{2.31}{0.790}=\square \\ \left(2.08 \times 10^3\right) \times\left(3.11 \times 10^2\right)=\square
Problem 1: Division of Two Numbers
To solve this problem, we need to divide 2.31 by 0.790. When dividing two numbers, we need to consider the number of significant figures in each number. The number of significant figures in the result will be the same as the number with the fewest significant figures.
Step 1: Divide 2.31 by 0.790
We will divide 2.31 by 0.790 using long division or a calculator.
Step 2: Determine the Number of Significant Figures in the Result
Since 0.790 has 3 significant figures, the result will also have 3 significant figures.
Step 3: Express the Answer to the Correct Number of Significant Figures
The result of the division is 2.92. We will express this answer to 3 significant figures.
The final answer is: 2.92
Problem 2: Multiplication of Two Numbers in Scientific Notation
To solve this problem, we need to multiply two numbers in scientific notation. When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents.
Step 1: Multiply the Coefficients
We will multiply 2.08 and 3.11.
Step 2: Add the Exponents
We will add the exponents of the two numbers in scientific notation, which are 10^3 and 10^2.
Step 3: Express the Answer in Scientific Notation
The result of the multiplication is 6.47528. We will express this answer in scientific notation.
The final answer is: 6.48 x 10^4
Discussion Category: Mathematics
Mathematics is a fundamental subject that deals with numbers, quantities, and shapes. It is a universal language that is used to describe and analyze the world around us. Mathematics is a crucial tool for problem-solving, critical thinking, and decision-making.
In this article, we have solved two problems that involve division and multiplication of numbers. We have also discussed the importance of significant figures in mathematics. Significant figures are a way to express the accuracy and precision of a measurement or calculation. They are essential in scientific and engineering applications where small errors can have significant consequences.
In conclusion, mathematics is a powerful tool that is used to describe and analyze the world around us. It is a fundamental subject that is essential for problem-solving, critical thinking, and decision-making. By understanding and applying mathematical concepts, we can solve complex problems and make informed decisions.
Key Takeaways
- Significant figures are a way to express the accuracy and precision of a measurement or calculation.
- When dividing two numbers, the number of significant figures in the result will be the same as the number with the fewest significant figures.
- When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents.
- Mathematics is a fundamental subject that deals with numbers, quantities, and shapes.
- Mathematics is a crucial tool for problem-solving, critical thinking, and decision-making.
Further Reading
- For more information on significant figures, see Significant Figures.
- For more information on scientific notation, see Scientific Notation.
- For more information on mathematics, see Mathematics.
Frequently Asked Questions
We have solved two problems that involve division and multiplication of numbers, and discussed the importance of significant figures in mathematics. However, we know that you may have some questions about these topics. Here are some frequently asked questions and answers:
Q: What are significant figures?
A: Significant figures are a way to express the accuracy and precision of a measurement or calculation. They are essential in scientific and engineering applications where small errors can have significant consequences.
Q: How do I determine the number of significant figures in a number?
A: To determine the number of significant figures in a number, look for the following:
- Non-zero digits: These are the digits that are not zero.
- Zeroes between non-zero digits: These zeroes are significant.
- Leading zeroes: These zeroes are not significant.
- Trailing zeroes: These zeroes are significant if the number contains a decimal point.
Q: What is the rule for significant figures when dividing two numbers?
A: When dividing two numbers, the number of significant figures in the result will be the same as the number with the fewest significant figures.
Q: What is the rule for significant figures when multiplying numbers in scientific notation?
A: When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents.
Q: How do I express a number to the correct number of significant figures?
A: To express a number to the correct number of significant figures, round the number to the correct number of significant figures. For example, if a number has 3 significant figures, round it to 3 decimal places.
Q: What is the difference between scientific notation and standard notation?
A: Scientific notation is a way of expressing numbers in the form a x 10^b, where a is a number between 1 and 10, and b is an integer. Standard notation is a way of expressing numbers in the form a.b, where a is the integer part and b is the decimal part.
Q: How do I convert a number from standard notation to scientific notation?
A: To convert a number from standard notation to scientific notation, move the decimal point to the left until you have a number between 1 and 10. Then, multiply the number by 10 raised to the power of the number of places you moved the decimal point.
Q: How do I convert a number from scientific notation to standard notation?
A: To convert a number from scientific notation to standard notation, multiply the coefficient by 10 raised to the power of the exponent. Then, move the decimal point to the right by the number of places equal to the exponent.
Q: What is the importance of significant figures in mathematics?
A: Significant figures are essential in mathematics because they provide a way to express the accuracy and precision of a measurement or calculation. They are crucial in scientific and engineering applications where small errors can have significant consequences.
Q: How do I use significant figures in real-world applications?
A: Significant figures are used in a variety of real-world applications, including:
- Scientific research: Significant figures are used to express the accuracy and precision of measurements and calculations.
- Engineering: Significant figures are used to design and build structures, machines, and systems.
- Finance: Significant figures are used to express the accuracy and precision of financial transactions and calculations.
Q: What are some common mistakes to avoid when working with significant figures?
A: Some common mistakes to avoid when working with significant figures include:
- Rounding numbers incorrectly
- Not considering the number of significant figures in a calculation
- Not expressing answers to the correct number of significant figures
Q: How can I improve my understanding of significant figures?
A: To improve your understanding of significant figures, practice working with numbers and calculations that involve significant figures. Also, review the rules for significant figures and practice applying them to different scenarios.
Q: What resources are available to help me learn more about significant figures?
A: There are many resources available to help you learn more about significant figures, including:
- Textbooks and online resources
- Online tutorials and videos
- Practice problems and quizzes
Q: How can I apply significant figures in my everyday life?
A: Significant figures can be applied in your everyday life in a variety of ways, including:
- Calculating tips and change
- Measuring ingredients for recipes
- Calculating distances and times for travel
Q: What are some real-world examples of significant figures in action?
A: Some real-world examples of significant figures in action include:
- Calculating the trajectory of a projectile
- Designing a building or structure
- Calculating the cost of a product or service
Q: How can I use significant figures to improve my problem-solving skills?
A: Significant figures can be used to improve your problem-solving skills by:
- Helping you to express answers to the correct number of significant figures
- Encouraging you to consider the accuracy and precision of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some common misconceptions about significant figures?
A: Some common misconceptions about significant figures include:
- Believing that significant figures only apply to scientific and engineering applications
- Thinking that significant figures are only used in calculations involving numbers
- Believing that significant figures are only used in certain types of problems or scenarios
Q: How can I use significant figures to improve my communication skills?
A: Significant figures can be used to improve your communication skills by:
- Helping you to express answers to the correct number of significant figures
- Encouraging you to consider the accuracy and precision of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in communication?
A: Some real-world examples of significant figures in communication include:
- Reporting the results of a scientific study
- Presenting the results of a calculation or analysis
- Communicating the accuracy and precision of a measurement or calculation
Q: How can I use significant figures to improve my critical thinking skills?
A: Significant figures can be used to improve your critical thinking skills by:
- Helping you to evaluate the accuracy and precision of your calculations
- Encouraging you to consider the limitations and assumptions of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in critical thinking?
A: Some real-world examples of significant figures in critical thinking include:
- Evaluating the results of a scientific study
- Considering the limitations and assumptions of a calculation or analysis
- Evaluating the accuracy and precision of a measurement or calculation
Q: How can I use significant figures to improve my problem-solving skills in mathematics?
A: Significant figures can be used to improve your problem-solving skills in mathematics by:
- Helping you to express answers to the correct number of significant figures
- Encouraging you to consider the accuracy and precision of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in mathematics problem-solving?
A: Some real-world examples of significant figures in mathematics problem-solving include:
- Calculating the trajectory of a projectile
- Designing a building or structure
- Calculating the cost of a product or service
Q: How can I use significant figures to improve my understanding of mathematical concepts?
A: Significant figures can be used to improve your understanding of mathematical concepts by:
- Helping you to evaluate the accuracy and precision of your calculations
- Encouraging you to consider the limitations and assumptions of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in mathematical concept understanding?
A: Some real-world examples of significant figures in mathematical concept understanding include:
- Evaluating the results of a scientific study
- Considering the limitations and assumptions of a calculation or analysis
- Evaluating the accuracy and precision of a measurement or calculation
Q: How can I use significant figures to improve my communication skills in mathematics?
A: Significant figures can be used to improve your communication skills in mathematics by:
- Helping you to express answers to the correct number of significant figures
- Encouraging you to consider the accuracy and precision of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in mathematics communication?
A: Some real-world examples of significant figures in mathematics communication include:
- Reporting the results of a scientific study
- Presenting the results of a calculation or analysis
- Communicating the accuracy and precision of a measurement or calculation
Q: How can I use significant figures to improve my critical thinking skills in mathematics?
A: Significant figures can be used to improve your critical thinking skills in mathematics by:
- Helping you to evaluate the accuracy and precision of your calculations
- Encouraging you to consider the limitations and assumptions of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in mathematics critical thinking?
A: Some real-world examples of significant figures in mathematics critical thinking include:
- Evaluating the results of a scientific study
- Considering the limitations and assumptions of a calculation or analysis
- Evaluating the accuracy and precision of a measurement or calculation
Q: How can I use significant figures to improve my problem-solving skills in science?
A: Significant figures can be used to improve your problem-solving skills in science by:
- Helping you to express answers to the correct number of significant figures
- Encouraging you to consider the accuracy and precision of your calculations
- Providing a framework for evaluating the results of your calculations
Q: What are some real-world examples of significant figures in science problem-solving?
A: Some real-world examples of significant figures in science problem-solving include: