Scientific Measurement Chapter 3

Measurement & Uncertainty Making measurements and performing calculations with measurements is very important in science and many other fields Any measurement has a number with a unit How do you know if a measurement is true? Are there limits to measurement?

Scientific Notation A convenient way of writing very large and very small numbers A way to indicate significant figures Standard (Decimal) notation 0.00000000000030 m (radius of H atom) Scientific notation 3.0 x 10-13 m coefficient x 10 power first digit must be from 1 to 9 1.65 x 10 4 Correct format? 0.053 x 10 -2 Correct format? 12.63 x 10 15 Correct format?

Calculations with Scientific Notation Review scientific notation in your text Read pages R56-57, Appendix C Your calculator uses a special key to enter scientific notation EE, E, Exp, Sci These keys mean “x 10exp” to your calculator Do not use 10^

Calculations with Scientific Notation How to enter 6.022 x 1023 6.022 2nd EE 23 Your calculator screen should show 6.022E23

Calculations with Scientific Notation Calculate 6.52 x 1018 ÷ 4.91 x 10-5 6.52 2nd EE 18 ÷ 4.91 -5 ENTER = 1.33…..E23

Accuracy, Precision, & Error Accuracy and precision are not the same thing Accuracy how close a measurement is to the true value (actual or accepted value) Precision how close measurements agree how exact a measurement is Example: a centigram balance (0.01g) is more precise than a decigram balance (0.1g) Error difference between actual and experimental value

Accuracy & Precision

Accuracy & Precision To evaluate accuracy of a measurement: compare measurement to true value To evaluate precision of a measurement: compare values of two or more repeated measurements

Uncertainty in Measurement All measurements are approximations All measurements contain error, so we can only report numbers that we know for sure (certain) The certainty of a measurement is determined by the precision of the measurement Significant figures are used to reflect certainty of measured value

Uncertainty in Measurement Digital instruments (like our electronic scales) estimate the final digit Example: 5.67 g In this measurement, the 7 is estimated by the scale The uncertainty of the scale is the smallest division reported by the scale (0.01 g) Recording the measurement with its uncertainty: 5.67 ± 0.01 g

Significant Figures All digits that are known, plus one last estimated digit Represent certainty of a measurement Must be handled properly in calculations to prevent overstating precision Review rules to determine significant figures (p. 66-67)

Significant Figures in Measurement

Rules for Determining Significant Figures All non-zeros YES Zeros between non-zeros YES Zeros at the beginning of a # NO Zeros at the end, to right of “.” YES Final zeros without “.” NO Final zeros with “.” YES

Significant Figures in Calculations Multiplication & Division Result must have the same # of s.f. as the measurement with the fewest s.f. 6.221 cm x 5.2 cm = 32.3492 cm2 → 32 cm2 Addition & Subtraction Result may not have more decimal places than the number with the fewest decimal places 20.4 + 1.322 + 83 = 104.722 → 105

Uncertainty in Measurement An error due to limitations of the instrument For a digital instrument +/- the smallest digit 62.56g +/- 0.01 g For an analog instrument +/- the estimated digit See example

Determining Error Error: the difference between the accepted and experimental measurement Example: Water was measured to boil at 101.5ºC The known bp of water is 100.0ºC Calculate the error in the measurement

Percent Error Error is often better understood as a percent of the true value Note that the numerator is absolute value!

3.2 International System of Units SI units (System International) used to be called the metric system Standard units used in science

Metric Prefixes* *Memorize these prefixes and their factors

Common Units of Volume

Mass vs. Weight Mass is a measure of matter Anything that occupies space has mass Weight is a force The force of gravity acting on a mass

Temperature Scales Used in Science Kelvin (Absolute Temperature) Absolute zero 0º K = -273.15º C no negative temps Celsius 0 C = +273.15 K A Kelvin degree and a Celsius degree have the same size

Conversions Between the Celsius and Kelvin Scales We will not use the Farenheit scale!

Energy Units of Energy Energy is the capacity to do work or to produce heat. The joule (J) is the SI unit of energy. One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C.

The Joule Pronunciation Guide NO NO YES!

Energy can be converted into other forms, but the units are still joules (J) This house is equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances.

3.3 Conversion Problems Conversion Factors Ratio of two equivalent measurements 1 dozen = 12 items

Dimensional Analysis When solving problems, units must be consistent Unit conversion are often necessary Use conversion factors Problem: Determine how many centimeters are in 1 yd. 1 yd x 36.0 in x 2.54 cm = 91.44 cm 1 yd 1 in

3.4 Density Density is the ratio of mass to volume Density is an intensive property Density of a pure substance is constant at a given temperature

Density Depends on temperature Units temp  density What if temp decreased? Units g/cm3 or g/mL for solids & liquids g/L for gases