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, thedigits 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 FiguresRule #1. Nonzero digits are always significant.6.24g ________sig figs23.4814mm _______ sig figs27.85 kg _______ sig figs67 seconds _______ sig figs

Rule #2 Zeroes appearing between nonzero digits are significant.8708_________ sig figs40.7 _________ sig figs173902.24_____sig figs2300.5________ sig figs

Rule # 3 Leading zeroes do not count as significant figures0.7 g________ sig figs0.00878L____ sig figs0.026 dL ______ sig figs0.15m________sig figs

Rule #4 Zeroes at the end of a number are significant only if the number contains a decimal point.50 g________ sig figs2850m______ sig figs7.50mm______ sig figs400.0 mL______sig figs0.00587 kg____sig figs

Rules for RoundingIf 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

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 SubtractionRule #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 CheckCarry 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