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state-rules-for-significant-figures-addition

🚀 In mathematics, particularly in the context of measurement, significant figures are crucial for conveying the precision of a number. When performing addition with numbers that have different numbers of significant figures, the result should be reported with the same number of decimal places as the number with the least decimal places. This ensures that the precision of the result reflects the least precise measurement used in the calculation.

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 trailing zeros in the decimal portion. For example, in the number 0.00456, there are three significant figures: 4, 5, and 6.

Rules for Addition

When adding numbers, the result should be rounded to the least number of decimal places of any number in the operation. For instance, if you add 12.11 (two decimal places) and 0.3 (one decimal place), the result should be rounded to one decimal place, as 0.3 has the least number of decimal places.

Rounding Off

When rounding off, if the digit to the right of the last significant figure is 5 or greater, round up. If it is less than 5, round down. This ensures that the final result maintains the appropriate level of precision.

Key Points

  • 🎯 Significant figures indicate the precision of a measurement.
  • 🎯 In addition, the result should have the same number of decimal places as the measurement with the least decimal places.
  • 🎯 Rounding is essential to maintain the correct number of significant figures in the result.

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Examples:💡

Example 1: Add 12.11 and 0.3.

Solution:

Step 1: Identify the number of decimal places in each number: 12.11 has 2 decimal places, and 0.3 has 1 decimal place.

Step 2: Perform the addition: 12.11 + 0.3 = 12.41.

Step 3: Round the result to the least number of decimal places (1 decimal place): 12.41 rounds to 12.4.

Common Mistakes

  • Mistake: Students often ignore the decimal places when adding numbers with different significant figures.

    Correction: Always check the number of decimal places in each number before performing the addition.

  • Mistake: Rounding incorrectly after addition, especially when the digit to round is 5.

    Correction: Remember the rounding rules: round up if the next digit is 5 or greater, and round down if it is less than 5.

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