IV. Significant figures

Recall from yesterday… Significant Digits(figures) – includes all of the digits that are known + a last digit that is estimated

A. Significant Figures Measurements must always be reported to correct # of sig. figs. Calculated answers depend on the # of sig figs in the values used in the original measurements.

B. Exact vs. Inexact Numbers Exact numbers – numbers known exactly (by definition or by counting) Ex: one dozen (12), one foot (12 inches), 1 teacher in the room Have INFINITE significant figures Inexact numbers – values with some uncertainty; anything measured using a piece of equipment (balance, graduated cylinder, beaker, etc.) Ex: mass of penny = 3.03 grams

C. Precision vs. Accuracy Precision – how closely individual measurements agree (repeatability) Accuracy – how closely individual measurements agree with the correct or “true” value (bull’s-eye) GREATER ACCURACY of an instrument means more SIGNIFICANT FIGURES.

D. Significant Figure Rules RULE 1: all NONZERO numbers are significant Examples: 96 g = 2 sig figs 61.4 cm = 3 sig figs 0.52 mL = 2 sig figs

D. Rules Continued Pacific Atlantic If the decimal is present, start at the Pacific If the decimal is absent, start from the Atlantic Find the first # that is not a zero and the rest are significant

For Example… 0.00456 cm 1.000008 dL 1345 mL 10450 mm 1345000 km 1.000345 dag 1.000008 dL 10450 mm 1000430 hg 0.000765 Mm

You Try! How many sig figs in the following: Examples: a) 1001 km b) 34.00 m c) 129,870 m d) 0.003 km e) 1.003 f) 0.0072561 g g) 20,000 cm h) 0.0023 g Number of Significant Figures: a) 4 b) 4 c) 5 d) 1 e) 4 f) 5 g) 1 h) 2

E. Rounding Rules When the rounding number is greater than or equal to 5: round up. Ex: 5.76 = 5.8 4.89 = 4.9 When the rounding number is less than 5: round down. Ex: 5.24 = 5.2 4.12 = 4.1

F. Multiplying & Dividing With Sig Figs Rule: when multiplying or dividing measurements, round final answer to the smallest # of significant figures in the original measurements.

CALCULATIONS WITH SIG FIGS Examples: 1. 2.03 cm x 36.00 cm = 73.08 cm² = 73.1 cm² 2. (1.13 m)(5.126122m) = 5.7925178 m² = 5.79 m² 3. 49.6000 cm² / 47.40 cm = 1.0464135 cm = 1.046 cm

G. Adding & Subtracting Sig Figs Rule: When adding or subtracting, round the answer to the same number of decimal places as the measurement with the smallest number of decimal places.

CALCULATIONS WITH SIG FIGS Examples: 1) 677.1 cm 2) 34.231 g 3) 16.45 cm 39.24 cm 6.709 g - 8.329 cm + 6.232 cm + 18.20 g 8.121 cm 722.572 cm 59.140 g = 722.6 cm = 59.14 g = 8.12 cm

Practice Addition Multiplication 165.5 cm + 8 cm + 4.37 cm = 2.6 cm x 3.78 cm = 177.87 cm = 178 cm 9.828 cm2 = 9.8 cm2