2.4: Background - Significant Figures in Calculations

Once we have significant figures from measurements, we need to keep track of them when those numbers are used in further calculations. There are many rules for different situations, but for this lab, we will focus on multiplication/division and addition/subtraction.

• When multiplying and dividing, report the least number of significant figures.
  • Consider the equation: \(1.42*2.0=2.84\)
    • 1.42 has three significant figures. 2.0 has two significant figures. We need to round 2.84 to 2.8.
  • Thus, \(1.42*2.0=2.8\) when reporting the correct number of significant figures.
• When adding and subtracting, count decimal places and report to the least number of decimal places.
  • For example: \(1002.345 + 1.2796 = 1003.6246\)
    • 1002.345 has three decimal places. 1.2796 has four decimal places. We need to round to three decimal places.
  • Thus, \(1002.345 + 1.2796 = 1003.625\) when accounting for significant figures.
• When rounding, look at the number to the right of the last significant digit or decimal place:
  • if 0 to 4, just drop the digits not needed.
    • 2.84 was rounded to 2.8.
  • If 5 to 9, round the last significant digit up by one.
    • 1003.6246 was rounded to 1003.625.

Keeping track of significant figures in calculations communicates how certain we can be about a number based on the measured data used.

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