Unit 1 Significant Figures in Measurements

Scientific Measurements When using a scale you read the value on the closest line and ONE guess.

You Try! Measure the length and width of your paper in mm. Record the correct number of significant figures.

Scientific Measurements Measurement includes value of closest line plus one more decimal “guess”. Here it would be 4.7x. We know it is a little more than 4.7, so the “x” is the guess.

Scientific Measurements Liquid measurements taken from bottom of meniscus.

Scientific Measurements Measurement includes value of closest line plus one more decimal “guess”. 6.6x mL I would say 6.61 mL

Scientific Measurements For digital devices, record ALL decimals Temperature measurement is 13.0°C (not 13°C)

SIGNIFICANT FIGURES Read each measurement: 28 mL 28.3 mL 28.32 mL

Precision v. Accuracy Precision –how closely individual measurements agree (repeatability) Accuracy – how closely individual measurements agree with the correct or “true” value (bullseye)

Significant Figures 56,400,000 Is there a decimal? PACIFIC (Present) ATLANTIC (Absent) Start from LEFT & count all #s from first nonzero 0.003100 Start from RIGHT & count all #s from first nonzero 56,400,000 4 sig figs 3 sig figs

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 L f) 6.02 x 1023 atoms g) 20,000 cm h) 0.0023 g Number of Significant Figures: a) 4 b) 4 c) 5 d) 1 e) 4 f) 3 g) 1 h) 2

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

Rounding Round each of these to 2 sig figs: Examples: a) 34.00 m b) 34,000 m c) 129,870 m d) 0.003 km e) 1.003 L f) 6.02 x 1023 atoms g) 20,000 cm h) 1001 km Number of Significant Figures: a) 34 m b) 34,000 m c) 130,000 m d) 0.0030 km e) 1.0 L f) 6.0 x 1023 atoms g) 2.0 x 104 cm h) 1.0 x 103 km

CALCULATIONS WITH SIG FIGS RULE: When multiplying or dividing, round the final answer to the measurement with the smallest number of significant figures. 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

CALCULATIONS WITH SIG FIGS RULE: When adding or subtracting, round the answer to the smallest number of decimal places. Examples: 1) 677.1 cm 39.24 cm + 6.232 cm 722.572 cm = 722.6 cm

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

CALCULATIONS WITH SIG FIGS Summary Multiplying or dividing: round to the measurement with the smallest number of significant figures. Adding or subtracting: round the answer to the smallest number of decimal places.

You Try! Calculate the area (length x width) of your paper using the correct number of sig figs.