Significant Figures

Understanding Significant Figures

  • Significant Figures refer to the digits in a number that carry meaning contributing to its precision.
  • This concept is used frequently in various math and science fields to express values more accurately.
  • Each digit in a number has a position and can be a significant or non-significant figure. For instance, In the number 0.004560, the significant figures are 456.

Notation and Representation

  • The Leading Zeroes in a number (like 0.0064) are not considered significant. In this example, 6 and 4 are the only significant digits.
  • All Non-zero digits are considered significant. For instance, in the number 456, all three digits are significant.
  • Any Zeroes between significant figures are also considered significant. For instance, in 5003, all four digits are significant.
  • Trailing Zeroes in a decimal number are significant. For example, in 45.00, all four digits are significant.

Rounding to Significant Figures

  • To round off a number to a certain number of significant figures, identify the final digit that will remain after rounding.
  • If the digit following this one is less than 5, the last retained digit stays the same. If it’s 5 or more, increase the last retained digit by one.
  • For example, if you’re rounding 89.647 to three significant figures, it would be 89.6 because the digit following 6 (which is 4) is less than 5.

Problem Solving with Significant Figures

  • Using significant figures correctly is crucial when doing calculations to ensure accurate results.
  • In multiplication and division, your answer should have as many significant figures as the original number with the least significant figures.
  • In addition and subtraction, the result should have as many decimal places as the number with the least decimal places.

Common Mistakes to Avoid

  • Misidentifying significant and non-significant digits, especially when dealing with zeroes.
  • Not rounding correctly to the required number of significant figures.
  • Failing to maintain the correct number of significant figures in calculations.
  • Making mistakes in understanding the role of significant figures in maintaining accuracy in mathematical operations.