Significant Figures Uncertainty in Measurement Because Nothing in

Significant Figures

Uncertainty in Measurement Because Nothing in physics is ever certain…

Measurement in Science Quantitative observations (measurements) must consist of two parts: a number and a unit Mrs. Petraroi is 5 feet 8 inches tall What would happen if we did not have units? ?

Measuring Volume in the Lab Volume is measured from the bottom of the meniscus

Uncertainty in Measurement Any measurement involves an estimate and thus is uncertain to some extent

Uncertainty in measurement If 5 different people took a measurement of a pin, we could have 5 different measurements: Person 1 2 3 4 5 Measurement 2. 85 cm 2. 84 cm 2. 86 cm 2. 85 cm 2. 86 cm

Uncertainty in measurement If 5 different people took a measurement of a pin, we could have 5 different measurements: Person 1 2 3 4 5 Measurement 2. 85 cm 2. 84 cm 2. 86 cm 2. 85 cm 2. 86 cm The first two digits are the same regardless of who made the measurement (these are called certain numbers))

Uncertainty in measurement If 5 different people took a measurement of a pin, we could have 5 different measurements: Person 1 2 3 4 5 Measurement 2. 85 cm 2. 84 cm 2. 86 cm 2. 85 cm 2. 86 cm The last digit varies; it is called the uncertain number

You Try… Take the Volume of the liquids in the next two graduated cylinders 1 minute to discuss and write your answer

1. Uncertainty in Measurement Take the Volume! (Always take a measurement to the first uncertain number. )

1. Uncertainty in Measurement To be correct, your answer must be in the following range: 56. 0 -56. 9 m. L

2. Uncertainty in Measurement Take the Volume! (Always take a measurement to the first uncertain number. )

2. Uncertainty in Measurement To be correct, your answer must be in the following range: 8. 40 -8. 49 m. L

Rules for counting Significant Figures 1. Nonzero numbers always count Ex: 1457 has 4 sig figs

Rules for counting Significant Figures 1. Nonzero numbers always count 2. Leading zeros never count Ex: 0. 0025 has 2 sig figs

15, 677

0. 0391

Rules for counting Significant Figures 1. Nonzero numbers always count 2. Leading zeros never count 3. Captive zeros always count Ex: 1. 008 has 4 sig figs

506

0. 06002

Rules for counting Significant Figures 1. 2. 3. 4. Nonzero numbers always count Leading zeros never count Captive zeros always count Trailing zeros only count if the number contains a decimal point Ex: 100 has only 1 sig fig 100. has 3 sig figs

0. 4700

5, 000

Rules for counting Significant Figures 1. 2. 3. 4. Nonzero numbers always count Leading zeros never count Captive zeros always count Trailing zeros only count if the number contains a decimal point 5. Exact numbers (have an unlimited number)

What is an exact number? ? Numbers that are determined by counting: 10 experiments 8 molecules Definitions 1 inch = 2. 54 cm

Significant Figures and Rounding If the digit to be removed: A. is less than 5, the preceding digit stays the same (1. 33 1. 3) B. is equal to or greater than 5, the preceding digit is increased by 1 (1. 36 1. 4)