Units, Measurement, Significant Figures & Conversions Physics

SI Units The SI Units we will be concerned with mostly are: QuantityUnit Length/Distance Time Mass Temperature meter [m] second [s] kilogram [kg] Kelvin [K]

SI Units All of our other units will be based on meters, kilograms, seconds, and Kelvins. This is referred to as the mks unit system Other systems: cgs; ft/lb/s

Making Measurements All measurements must contain both 1. A number 2. A unit Measured values are reported such that only the last digit is uncertain. ALL digits of a measurement, including the last one, are called significant figures. Aka: Sig figs

Measuring Length Length measurements are made in units of meters.

Length Measurements  What is the measurement? A) m B) 12 m C) 12.9 m

Length Measurements  What is the measurement? A) 10.3 m B) m C) 10 m

Length Measurements  What is the measurement? A) 11.5 m B) m C) 11 m

Sig Fig Rules All nonzero digits are significant. Ex: 2.54 has ____ sig figs Ex: has ____ sig figs Zero Rules A zero is significant when it appears between two nonzero digits Ex: 2.04 has ____ sig figs Ex: has ____ sig figs

Sig Fig Rules Zero Rules cont. A zero is significant when it appears at the end of a number AND to the right of the decimal Ex: has ____ sig figs Ex: 17.0 has ____ sig figs 4 3

Sig Fig Rules Zero Rules cont. A zero is NEVER significant when it appears in front of a number Ex: has ____ sig figs Ex: 0.09 has ____ sig fig 4 1

Sig Fig Rules Zero Rules cont. A zero is SOMETIMES significant when it appears at the end of a number AND to the left of the decimal For this course, assume these zeros ARE NOT significant unless you read “precisely” or “exactly” in front of the number Ex: 20 has ____ sig fig Ex: 3400 has ____ sig figs 1 2

Sig Fig Rules A good rule-of-thumb for the zeros in sig figs is this: Convert the number to scientific notation and if the zeros drop out then they are not significant Ex: = x So it has 4 sig figs Ex: 3400 = 3.4 x 10 2 So it has 2 sig figs

Try it! How many sig figs are in each of the following? A) 3B) 6C) 7

Try it! How many sig figs are in each of the following? A) 2B) 3C) 4

Try it! How many sig figs are in each of the following? , A) 5B) 9C) 11

Try it! How many sig figs are in each of the following? , A) 2B) 8C) 9

Try it! How many sig figs are in each of the following? , A) 2B) 4C) 5

Accuracy & Precision Two types of numbers in scientific work: 1. Exact numbers 2. Inexact numbers Measurements are inexact due to equipment and human error. Precision & accuracy are used to describe the uncertainty of measured values.

Accuracy & Precision Precision refers to how reproducible individual measurements are Accuracy refers to how closely individual measurements agree with the “true” or accepted value

Accuracy & Precision Precise but not accurate Accurate but not precise

Accuracy & Precision Neither accurate nor precise Both accurate and precise GOOD BAD

Unit Conversions Notes on board

Try It! 183 cm equals how many meters? First, choose a conversion factor: A)B)C) Then do the calculation: A) 1.83 m B) 18.3 mC) m 1 m 100 cm 10 mm 1 cm 1,000 m 1 km

Try It! 8,700 milligrams is how many grams? First, choose a conversion factor: A)B)C) Then do the calculation: A) 0.87g B) 87.0 gC) 8.7 g 1000 mg 1 g 1000 kg 1 g 1000 mg

Try It! 4.3 Astronomical Units (A.U.) is equal to how many kilometers? First, choose a conversion factor: A)B)C) Then do the calculation: A) 6.4 km B) x 10 8 km C) 6.4 x 10 8 km 1 A.U. 149,597,870.7 km 1 A.U. 149, m 1 A.U.