Significant Figures

In science, measured values are reported in terms of significant figures. Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

If we look back at this figure from yesterday, the digits we are certain of are 36. The final measurement, depending on who is reading the cylinder, could be 36.5, 36.6, and even 36.7 mL.

Rules for Determining Significant Figures Rule #1. Nonzero digits are always significant. 6.24g ________sig figs 23.4814mm _______ sig figs 27.85 kg _______ sig figs 67 seconds _______ sig figs

Rule #2 Zeroes appearing between nonzero digits are significant. _________ sig figs 40.7 _________ sig figs 173902.24_____sig figs 2300.5________ sig figs

Rule # 3 Leading zeroes do not count as significant figures 0 Rule # 3 Leading zeroes do not count as significant figures 0.7 g________ sig figs 0.00878L____ sig figs 0.026 dL ______ sig figs 0.15m________sig figs

Rule #4 Zeroes at the end of a number are significant only if the number contains a decimal point. 50 g________ sig figs 2850m______ sig figs 7.50mm______ sig figs 400.0 mL______sig figs 0.00587 kg____sig figs

Rules for Rounding If the digit immediately to the right of the last significant figure you want to retain is: Less than 5 ------ the last significant digit should stay the same. Example: Round 18.32 m to 3 significant figures. Since the 2 is less than 5, you should round to __________ m

Round 42.88 g to 3 significant figures. If the digit immediately to the right of the last significant figure you want to retain is: 5 or greater --------- the last significant figure should increase by 1. Example: Round 42.88 g to 3 significant figures. Since 8 is greater than 5, you should round to __________ g

Addition or Subtraction Rule #1: Whenever you add or subtract measurements, your answer should have as many DECIMAL PLACES as the measurement with the LEAST number of DECIMAL PLACES. EXAMPLE: 23.445 g + 7.83 g = 31.275 g 31.28 g

Rule#2: Whenever you multiply or divide measurements, your answer should have as many SIGNIFICANT FIGURES as the measurement with the LEAST number of SIGNIFICANT FIGURES. EXAMPLE: 1.342 cm × 5.5 cm = 7.381 cm2 7.4 cm2

Study Check Carry out the following calculations and give the answer with the correct number of significant figures: 125.76/11 5.44 - 2.6103 2.81 x 4.21