Uncertainty in Measurement

How confident are we in our measurements? Are they ACCURATE? Are they PRECISE? How many of the numerals in the measurement are SIGNIFICANT DIGITS?

Accuracy Precision Closeness of a single value to the true value Closeness of a set of values to each other

Precision and Accuracy

Uncertainty in Measurement All scientific measures are subject to error. The number of digits reported reflect the accuracy of the measurement and the precision of the measuring device. Significant Figures (Sig Figs) are all the figures known with certainty plus one extra uncertain figure.

Uncertainty in Measurement Instrument error Human error meniscus

Measurement on Metric Ruler 93.55 cm 97.18 cm

Rules: Significant Figures (Sig Figs) All non-zero numbers are significant. Ex) 3.45 (3 sig fig) Zeros between non-zero numbers are significant. Ex) 4,503 (4 sig fig) Zeros to the left of the first non-zero digit are not significant. Ex) 0.0003 (1 sig fig) Zeros to the right of a nonzero digit are significant IF the number contains a decimal point. Ex) 1.90 Ex) 10,300

Significant Figures (Sig Figs) 1.23 grams = 3 0.000123 grams = 3 2.0 grams = 2 0.020 grams = 2 100 grams = 1 100. grams = 3

How many Significant Figures 0.00821 630 5020 9102 7.200 x 102

How many Significant Figures 0.00821 630 5020 9102 7.200 x 102 Three Two Four

How many Significant Figures 0.09430 5760 5002 5200 1.30 x 105

How many Significant Figures 0.09430 5760 5002 5200 1.30 x 105 Four Three Two

Rounding off If the first insignificant digit is > 5 round up < 5 round down

Round off to three significant digits 546847

Round off to three significant digits last significant 546847 first insignificant

Round off to three significant digits 547000 Round up 546847 or 546000 Round down

Round off to three significant digits 547000 Round up 546847 546000

Round off to three significant digits 6876 6874 544.5 321.5

Round off to three significant digits 6876 6874 544.5 321.5 6880 6870 545 322

Scientific Notation For extremely large or small numbers Powers of 10 Ex) Speed of light is 30,000,000,000 cm/s Move decimal to the left 10 spaces 30,000,000,000 cm/s 3 x 1010 cm/s Ex) Wavelength of yellow light is 0.000059 cm Move decimal to the right 5 spaces 0.000059 cm 5.9 x 10-5 cm

Scientific Notation Correct Scientific Notation: 5.20 x 104 Incorrect Scientific Notation: 520 x 102 Practice: Write in Scientific Notation. 6,200,000,000,000,000 6.2 x 1015 8,201 8.201 x 103 0.000000074 7.4 x 10-8 0.000340 3.40 x 10-4

Significant Figures in Calculations Fewest significant digits 5.231 x 2.7 = 14

Significant Figures In any calculation, the results are reported to the fewest significant figures