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state-rules-for-significant-figures-multiplication

🚀 Significant figures are essential in scientific measurements, as they convey the precision of a measurement. When performing multiplication with numbers that have different numbers of significant figures, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures. This ensures that the precision of the least precise measurement dictates the precision of the final result, thus avoiding misleading conclusions from overly precise answers.

Theory Explanation

Understanding Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number. When multiplying numbers, the rule is to determine the number of significant figures in each number and then apply the multiplication rule accordingly.

Identifying Significant Figures

To apply the multiplication rule for significant figures, first identify the number of significant figures in each of the numbers you are multiplying. For example, the number 0.0045 has two significant figures (the '4' and '5'), while 12.3 has three significant figures (the '1', '2', and '3').

Applying the Multiplication Rule

When you multiply numbers, the result should have the same number of significant figures as the number with the least significant figures. For instance, if you multiply 12.3 (3 significant figures) by 0.0045 (2 significant figures), the result should be rounded to 2 significant figures, as 0.0045 has the least significant figures.

Key Points

  • 🎯 Significant figures indicate the precision of a measurement.
  • 🎯 In multiplication, the final result should have the same number of significant figures as the measurement with the least significant figures.
  • 🎯 Count all non-zero digits, zeros between significant digits, and trailing zeros in decimal numbers when determining significant figures.

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Examples:💡

Multiply 12.3 by 0.0045.

Solution:

Step 1: Identify the significant figures: 12.3 has 3 significant figures and 0.0045 has 2 significant figures.

Step 2: Perform the multiplication: 12.3 * 0.0045 = 0.05535.

Step 3: Round the result to 2 significant figures (the least number of significant figures): 0.05535 rounded to 2 significant figures is 0.055.

Common Mistakes

  • Mistake: Students often report the result with more significant figures than the least precise measurement.

    Correction: Always check the number of significant figures in each measurement before multiplying and ensure the final answer matches the least number of significant figures.

  • Mistake: Ignoring leading zeros when counting significant figures.

    Correction: Remember that leading zeros do not count as significant figures; only count non-zero digits and zeros that are between significant digits or trailing in a decimal.

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