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 figuresStandard (Decimal) notation

0.00000000000030 m (radius of H atom)Scientific notation

3.0 x 10-13 mcoefficient x 10 power

first digit must be from 1 to 91.65 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• 2nd EE• -5• ENTER = 1.33…..E23

Accuracy, Precision, & Error

Accuracy and precision are not the same thingAccuracy

how close a measurement is to the true value (actual or accepted value)

Precisionhow close measurements agreehow exact a measurement isExample: a centigram balance (0.01g) is more precise than a decigram balance (0.1g)

Errordifference 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 ErrorError:

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

C 1.5 Error

C 100.0 - C 101.5 Error

valueaccepted - valuealexperiment Error

Percent Error

Error is often better understood as a percent of the true value

Note that the numerator is absolute value!

1.5%

100x 100.0

100.0 - 101.5 error %

100x accepted

accepted - alexperiment error %

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

• Celsius0 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!

EnergyUnits 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 JoulePronunciation 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

dozen 1

items 12or

items 12

dozen 1

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 V

md

Density

• Depends on temperaturetemp density

What if temp decreased?

• Unitsg/cm3 or g/mL for solids & liquids

g/L for gases