Chapter 3: Scientific Measurement 3.1: Measurements and Their Uncertainty.

Chapter 3: Scientific Measurement

3.1: Measurements and Their Uncertainty

I. Types of Measures• A. Qualitative: descriptive data, non-numerical

– Ex. Color, smell, feel of something

• B. Quantitative: definite data in number form

– Ex. Temperature in degrees

Write down two qualitative and two quantitative measurements you could make about your own hand.

II. Scientific Notation Review• Try These:

680 =

70.75 =

0.0063 =

III. Using your Calculator• A. To perform calculations

using scientific notation, you need to use the EE, EXP, or x10x button.

• B. For 3.5x103, you type 3.5E3

• Do not multiply by 10!

IV. Accuracy, Precision, Error• A. Accuracy: how close measurement is to actual

value

• B. Precision: how close measurements are to each other (consistency)

• C. Error: Numerical difference between accepted and experimental value

• D. Percent error: (error/accepted value) x 100

V. Are They Accurate or Precise?

Precise Neither Accurate/Precise

VI. Uncertainty in Measurements• A. Measurements always have some amount of

uncertainty based on the measuring device

• B. Correct measurements always have only one “estimated digit”

4.36 cm

VII. Significant Figures• A. Numbers that tell us important information• B. Rules:

1. All non-zero #’s [0.005468]2. Zeros between non-zero [202000]3. Zeros behind numbers [202.000]

(if any decimal is visible)4. Exactly defined #’s have infinite sig. figs. (ex. 60

minutes in a hour)

VIII. Examples• Identify which of the numbers in the following

values are significant.

2.5000 3000 205

100.0 0.00300 10.

IX. Sig. Figs. In Calculations• A. Addition/ Subtraction: round answer to least

number of decimals in problem

Ex. 12.52 + 1.2 = 13.72 rounded to 13.7

• B. Multiplication/ Division: round answer to least number of sig. figs in problem

Ex. 10.5 x 5.5 = 57.75 rounded to 58

X. Examples• Solve the following using significant figures.

4.5 + 3.31 = 5.00 – 2 =

10.0 x 2 = 15.00 ÷ 3.0 =

3.2 International System of Units

I. Units of• A. SI: International System of

Units, metric, based on multiples of 10

• B. Prefixes indicate size of measurement

• C. Kilo: 1000, Centi: 1/100, Milli: 1/1000

• D. Length: distance, measured in meters (m)

II. Units of

• A. Volume: space occupied by matter

• B. Measured in Liters (L) or Meters3 (m3)

• C. Meters3 used when calculating volume by length x width x height

III. Units of

• A. Mass: amount of matter, grams (g)

• B. Weight: force of gravity on mass

IV. Units of Temperature• A. Definition: degree of hotness or

coldness

• B. Temp. Scales– I. Celsius (ºC): freezing pt. water at

0°C, boiling pt. at 100°C– II. Kelvin (K): 273 degrees more than

Celsius, set by absolute zero (-273°C) – III. Kelvin = Celsius + 273

Galileo Thermometer

V. Units of Energy• A. Energy: capacity to do work or produce heat

• B. Units are calories (cal) or Joules (J)1 cal = 4.184 J

Food Calories are actually kilocalories (1000x bigger)!

3.3 Conversion Problems

I. Conversion Factors• A. Ratio of equal measurements

Ex. 12 inches = 1 foot, 60 seconds = 1 minute

• B. In metric system one measurement will usually be “root” (meter, gram, liter, etc.) other will have prefix

1 meter = 100 centimeters1 meter = 100 centimeters

II. Unit Cancellation (“Cross Method”)• 1. Make cross

• 2. Given info. on top left

• 3. Desired unit at end of cross

• 4. Starting unit in bottom right (to cancel)

• 5. Corresponding unit on top right

• 6. Enter numbers to make conversion factor

• 7. Multiply #’s on top, divide on bottom

III. Example• Convert 3.75 yards to inches.

IV. Complex Units• A. Ratio units (Miles/hour, gram/ml)• B. Need to change one or both units• C. Use bottom of cross for denominator unit• D. Ex. 20 miles/hour miles/minute

20 miles

hour

hour

minute

1

60= miles/minute0.3

V. Example• Convert 10.0 kilometers/hour meters/second.

3.4: Density

Floating in the Dead Sea

I. Determining Density• A. Density: mass/volume

• B. SI units are gram/centimeter3 or gram/milliliter

• C. Density increases as temp. decreases

•D. Water is exception, ice less dense than liquid water