Measurements and Calculations

1. Measurements and Calculations Where math becomes reality!

2. Measurement standards • Quantities such as: • Time • Distance or length • “weight” • Light brightness MANY standards of measure have been used over the years.

3. Do you recognize any of these units? • Millennium • Slug • Bushel • Kilogram • Calorie • Cubit • Foot-pound • Fahrenheit

4. Only 7 quantities can be measured directly! Quantity Base Unit • Time • Mass • Distance or length • Temperature • Amount of substance • Amount of electricity • Light brightness • Second • Kilogram • Meter • Kelvin • Mole • Ampere • Candela

5. ...everything else is calculated! • Speed • Current • Energy • Volume • Weight • Force • …Which we call “derived” units… • What do you think “modified” units might be?

6. “metric” system • Actually, called “SI” for systeme international • Also called, “kg-m-s” system for • Kilogram • Meter • Second • Should US officially adopt?

7. Refresher……

8. Precision • Measurements are as only as specific as the instrument being used. • Consider a ruler marked in whole inches OR a ruler marked in tenths of inches. • This is called the “precision” of the instrument and is indicated by the number of places used in writing the measurement.

9. For example…. • That ruler marked in whole inches can only be written down to the tenths place. • 10.5 • 1.7 • 8.3 • Matter of fact, since the “tenth” was estimated, anyway, it is called a “guess digit”.

10. How about the ruler marked in tenths? • Well, you could estimate in the hundredths place. • 10.58 • 1.46 • 0.58 • Consider the measurement 11.20 inches using that ruler……why write the “zero”?

11. Which numbers are significant? • All non-zeroes. • Zeroes between non-zeroes. • All zeroes to the right of a non-zero and the right of the decimal. • All zeroes to the right of non-zeroes and the left of the decimal IF…IF…IF the decimal is written to indicate that those zeroes were measured. (Easiest to use sci not for that.) • Counting numbers and constants do not count as sig figs.

12. Scientific Notation Refresher…. • The Arabic number system is based on 10! • 101 is one decimal place, right? • What about 10-3? • Let’s practice!

13. Whew! Let’s summarize… • Measured quantities are used to calculate other quantities of interest. • Those measurements come in a variety of scales and definitions, SO we all have to agree on a system. • Measurements are written in such a way as to indicate the precision of the instrument used.

14. Next…. • How does that precision get indicated when we calculate with the number? • In other words, if I’m calculating with two numbers: one is made to the tenths….another is measured to the thousandths, where should I round my answer? How precise can my calculation be?

15. Multiplying & Dividing • Your answer can be NO MORE precise than your worst measurement…. • Translation: your answer can have no more than the least number of sig figs as the measurements

16. Adding & Subtracting • Your answer can have the least number of DECIMAL PLACES as the least number in the measurements.

17. FINALLY……. • Accuracy is not the same as precision!?!*@! • Accuracy is expressed in terms of absolute and relative error. • Absolute error • The absolute value of the difference between the observed answer and the accepted answer. • Relative (percent) error • Absolute error divided by accepted answer *100 • ER = EA / accepted * 100

18. Gotta’ have examples • A sophomore measured the length of a football field to be 98.6 yards • Meanwhile, • A junior measured the length of a 15.0-cm pen to be 13.28cm. • Who is more precise? Who is more accurate?

19. WHEW!! • Scientific notation • SI units • Base units • Derived unit • Modified unit • Precision • Sig figs • Accuracy • Absolute error • Relative error