Express your answer to one significant figure and include the

Question

Express your answer to one significant figure and include the appropriale whit: Part B Expess year answer to two significant figures and include the appropriate units.

Answer

Step 1

Express your answer to one significant figure and include the

Step 2

Express your answer to one significant figure and include the

Step 3

Express your answer to one significant figure and include the

Answer

  • Part A: 0.9g
  • Part B: 7.9mL
  • Part C: 2.50g

Significant Figures Explained: Expressing Answers with Correct Precision

In the world of science and engineering, precision is paramount. Whether you’re calculating the dosage of a medication, determining the load a bridge can withstand, or measuring the components of a chemical solution, the accuracy of your measurements can significantly impact the outcomes. One fundamental concept that ensures this precision is the use of significant figures. Understanding and correctly applying significant figures in your calculations is crucial for expressing answers with the right level of accuracy. In this article, we’ll explore what significant figures are, why they matter, and how to use them effectively in your measurements and calculations.

What Are Significant Figures?

Significant figures (often abbreviated as “sig figs”) are the digits in a number that carry meaningful information about its precision. These include all non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number. For example, the number 0.004520 has four significant figures: 4, 5, 2, and the trailing zero.

Why Do Significant Figures Matter?

Using significant figures correctly ensures that the precision of your calculations matches the precision of your measurements. When performing mathematical operations, the precision of the result should not exceed the precision of the least precise measurement. This is crucial in scientific disciplines where the accuracy of data can influence experimental outcomes, safety standards, and overall reliability of results.

Rules for Identifying Significant Figures

Non-zero digits are always significant.

  • Example: 1234 has four significant figures.

Any zeros between significant digits are also significant.

  • Example: 1002 has four significant figures.

Leading zeros are not significant.

  • Example: 0.00123 has three significant figures.

Trailing zeros in a decimal number are significant.

  • Example: 2.300 has four significant figures.

Using Significant Figures in Calculations

Addition and Subtraction

When adding or subtracting numbers, the result should have the same number of decimal places as the measurement with the fewest decimal places.

  • Example:
    • 12.11 (two decimal places)
      • 0.134 (three decimal places)
    • Result: 12.24 (two decimal places)

Multiplication and Division

When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest significant figures.

  • Example:
    • 4.56 (three significant figures)
    • × 1.4 (two significant figures)
    • Result: 6.4 (two significant figures)

Expressing Answers to One Significant Figure

When required to express an answer to one significant figure, you must round your result to retain only the most significant digit.

  • Example:
    • Calculation result: 56.789
    • Expressed to one significant figure: 60

Expressing Answers to Two Significant Figures

When expressing an answer to two significant figures, round your result to retain the two most significant digits.

  • Example:
    • Calculation result: 3.456
    • Expressed to two significant figures: 3.5

Conclusion

Mastering the use of significant figures is essential for anyone involved in scientific, engineering, or mathematical fields. It ensures that your measurements and calculations reflect the true precision of your data, providing reliable and accurate results. By understanding the rules and applying them consistently, you can communicate your findings clearly and accurately, whether you’re conducting experiments, reporting research, or solving complex problems. So, next time you’re faced with a calculation, remember the importance of significant figures and express your answers with the correct precision.

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