CHAPTER 3: MEASUREMENT

ACCURACY AND PRECISION

Can never be exact Instrument marking can’t be fine enough Defective instrument Environmental conditions Use or read the instrument incorrectly The Limits of Measuring p PHYSICAL SCIENCE

How many measurements are exactly on the scale division? Almost None!

89 ABCDE A cm B cm C cm A cm B cm C cm D cm E cm D cm E cm Ruler

ABCDE A g B g C g A g B g C g D g E g D g E g Balance

34 ABCDE A g B g C g A g B g C g D g E g D g E g Balance

A B C D Graduated Cylinder A mL B mL C mL D mL A mL B mL C mL D mL

A B C D 2 3 A. 2.9 mL B. 2.5 mL C. 2.4 mL D. 2.2 mL A. 2.9 mL B. 2.5 mL C. 2.4 mL D. 2.2 mL Graduated Cylinder

D C B A Thermometer A °C B °C C °C D °C A °C B °C C °C D °C

A B C D Beaker A. 85 mL B. 60 mL C. 40 mL D. 23 mL A. 85 mL B. 60 mL C. 40 mL D. 23 mL

The accuracy of a measurement is an assessment of the measurement error The instrument and the user can also affect the accuracy Accuracy p PHYSICAL SCIENCE

accurate but not precise

Precision is an assessment of the exactness of a measurement When measuring with a metric instrument, estimate the measurement to 1/10 of the smallest decimal subdivision on the instrument scale Precision pp PHYSICAL SCIENCE

precise but not accurate

accurate and precise

Scientists evaluate the usefulness of their measurements by repeating them as many times as needed to see how they vary Random errors Systematic errors Repeatability p PHYSICAL SCIENCE

Significant Digits Using the concept of significant digits (SD), scientists have a way to indicate the precision of their measurements pp PHYSICAL SCIENCE

Identifying Significant Digits SD Rule 1: SDs apply only to measured data SD Rule 2: All nonzero digits in measured data are significant SD Rule 3: All zeros between nonzero digits are significant pp PHYSICAL SCIENCE

SD Rule 4: Decimal points define significant zeros SD Rule 5: A decimal point must follow an estimated zero in the one’s place pp PHYSICAL SCIENCE

Convert very large or small numbers into a product of a small number and a power of ten M × 10 n 1 ≤ M < 10; n is an integer Scientific Notation p PHYSICAL SCIENCE

Scientific Notation and Significant Digits According to SD Rule 4B, how many SDs does the measurement 3800 mm have? 3800 mm (WRONG!) 3.80 × 10 3 mm (RIGHT!) p PHYSICAL SCIENCE

Scientists have developed sophisticated methods for identifying the significant digits in calculated results Become familiar with the rules in Appendix E Math with Measurements p PHYSICAL SCIENCE

Mechanical tolerance—the “wiggle room” in parts that are made to fit together Engineers express tolerance as the desired dimension plus or minus (±) Using Measurements p PHYSICAL SCIENCE