Select The Correct Answer.What Is The Solution To The Problem Expressed To The Correct Number Of Significant Figures? ${ 15.11 + (142 \times 16.5) = ? }$A. 2,358 B. 2,358.1 C. 2,360 D. 2,400

by ADMIN 195 views

Introduction

Significant figures are a crucial concept in mathematics, particularly in numerical calculations. They represent the precision or accuracy of a measurement or a calculated value. In this article, we will explore the concept of significant figures and how to apply them to mathematical operations, specifically in the context of the given problem.

What are Significant Figures?

Significant figures are the digits in a number that are known to be reliable and certain. They are used to express the precision of a measurement or a calculated value. The number of significant figures in a value depends on the instrument or method used to obtain the value. For example, a ruler may have a precision of 1 mm, which means that the value obtained using the ruler has 3 significant figures (e.g., 12.5 mm).

Rules for Significant Figures

There are several rules for significant figures that must be followed when performing mathematical operations:

  1. Rounding: When rounding a value to a certain number of significant figures, the last digit is rounded up or down depending on the value of the digit immediately after it.
  2. Multiplication and Division: When multiplying or dividing two values, the result should have the same number of significant figures as the value with the fewest significant figures.
  3. Addition and Subtraction: When adding or subtracting two values, the result should have the same number of decimal places as the value with the fewest decimal places.

The Given Problem

The problem given is:

15.11+(142×16.5)=?{ 15.11 + (142 \times 16.5) = ? }

To solve this problem, we need to follow the rules for significant figures.

Step 1: Multiply 142 and 16.5

First, we need to multiply 142 and 16.5.

142×16.5=2343{ 142 \times 16.5 = 2343 }

However, we need to consider the significant figures of the values. The value 142 has 3 significant figures, and the value 16.5 has 3 significant figures as well. Therefore, the result of the multiplication should have 3 significant figures.

142×16.5=2340{ 142 \times 16.5 = 2340 }

Step 2: Add 15.11 and 2340

Next, we need to add 15.11 and 2340.

15.11+2340=2355.11{ 15.11 + 2340 = 2355.11 }

However, we need to consider the significant figures of the values. The value 15.11 has 4 significant figures, and the value 2340 has 4 significant figures as well. Therefore, the result of the addition should have 4 significant figures.

15.11+2340=2355.1{ 15.11 + 2340 = 2355.1 }

Conclusion

In conclusion, the solution to the problem expressed to the correct number of significant figures is:

15.11+(142×16.5)=2355.1{ 15.11 + (142 \times 16.5) = 2355.1 }

This result has 4 significant figures, which is the same number of significant figures as the value with the fewest significant figures.

Answer

The correct answer is:

B. 2,355.1

Note: The answer is rounded to 4 significant figures, as required by the problem.

Discussion

The concept of significant figures is crucial in mathematics, particularly in numerical calculations. It represents the precision or accuracy of a measurement or a calculated value. In this article, we explored the concept of significant figures and how to apply them to mathematical operations. We also solved the given problem and obtained the correct answer.

References

  • "Significant Figures" by Khan Academy
  • "Significant Figures" by Math Is Fun
  • "Significant Figures" by Wolfram MathWorld

Further Reading

  • "Significant Figures in Calculations" by Physics Classroom
  • "Significant Figures in Measurements" by Science Buddies
  • "Significant Figures in Engineering" by Engineering Toolbox
    Significant Figures Q&A =========================

Frequently Asked Questions about Significant Figures

Q: What are significant figures?

A: Significant figures are the digits in a number that are known to be reliable and certain. They are used to express the precision of a measurement or a calculated value.

Q: Why are significant figures important?

A: Significant figures are important because they help to convey the precision or accuracy of a measurement or a calculated value. They are used in scientific and engineering applications to ensure that calculations are accurate and reliable.

Q: How do I determine the number of significant figures in a value?

A: To determine the number of significant figures in a value, look for the following:

  • Non-zero digits: Non-zero digits are always significant.
  • Zeroes between non-zero digits: Zeroes between non-zero digits are significant.
  • Leading zeroes: Leading zeroes are not significant.
  • Trailing zeroes: Trailing zeroes are significant only if the value has a decimal point.

Q: What are the rules for significant figures in mathematical operations?

A: The rules for significant figures in mathematical operations are:

  • Rounding: When rounding a value to a certain number of significant figures, the last digit is rounded up or down depending on the value of the digit immediately after it.
  • Multiplication and Division: When multiplying or dividing two values, the result should have the same number of significant figures as the value with the fewest significant figures.
  • Addition and Subtraction: When adding or subtracting two values, the result should have the same number of decimal places as the value with the fewest decimal places.

Q: How do I handle significant figures in calculations with decimals?

A: When handling significant figures in calculations with decimals, follow these steps:

  • Determine the number of significant figures in each value: Determine the number of significant figures in each value in the calculation.
  • Round the values to the correct number of significant figures: Round the values to the correct number of significant figures based on the rules for significant figures.
  • Perform the calculation: Perform the calculation using the rounded values.

Q: What is the difference between significant figures and decimal places?

A: Significant figures and decimal places are related but distinct concepts.

  • Significant figures: Significant figures represent the precision or accuracy of a measurement or a calculated value.
  • Decimal places: Decimal places represent the number of digits after the decimal point in a value.

Q: How do I determine the number of decimal places in a value?

A: To determine the number of decimal places in a value, count the number of digits after the decimal point.

Q: What is the importance of significant figures in scientific and engineering applications?

A: Significant figures are crucial in scientific and engineering applications because they help to ensure that calculations are accurate and reliable. They are used to convey the precision or accuracy of a measurement or a calculated value, which is essential in scientific and engineering applications.

Q: How do I apply significant figures in real-world applications?

A: To apply significant figures in real-world applications, follow these steps:

  • Determine the number of significant figures in each value: Determine the number of significant figures in each value in the calculation.
  • Round the values to the correct number of significant figures: Round the values to the correct number of significant figures based on the rules for significant figures.
  • Perform the calculation: Perform the calculation using the rounded values.

Conclusion

Significant figures are a crucial concept in mathematics, particularly in numerical calculations. They represent the precision or accuracy of a measurement or a calculated value. In this article, we explored the concept of significant figures and how to apply them to mathematical operations. We also answered frequently asked questions about significant figures.

References

  • "Significant Figures" by Khan Academy
  • "Significant Figures" by Math Is Fun
  • "Significant Figures" by Wolfram MathWorld

Further Reading

  • "Significant Figures in Calculations" by Physics Classroom
  • "Significant Figures in Measurements" by Science Buddies
  • "Significant Figures in Engineering" by Engineering Toolbox