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Measurements and Calculations

Measurements and Calculations. Where math becomes reality!. Measurement standards. Quantities such as: Time Distance or length “weight” Light brightness MANY standards of measure have been used over the years. Do you recognize any of these units?. Millennium Slug Bushel Kilogram

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Measurements and Calculations

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  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 • a worldwide agreement among scientists to adopt this method of measurement. • Also called, “kg-m-s” system for • Kilogram • Meter • Second • Should US officially adopt?

  7. Refresher……

  8. Accuracy vs. Precision • Accuracy – how close a measured value is to an accepted value • Precision – how close a series of measurements compare to one another • Sucrose density – 1.59 g/mL

  9. 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.

  10. 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”.

  11. 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”?

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

  13. Scientific Notation • Two factors: • A number between 1 and 10 • 10 raised to a power (exponent) • Tells how many times the first factor must be multiplied by 10 • Positive exponent – larger than 1 (move decimal to right) • Negative exponent – smaller than 1 (move decimal to left) • Examples: 1392000 – 1.392 x 106 0.000000028 – 2.8 x 10-8

  14. Which numbers are significant? • All non-zeroes. 72.3 • Zeroes between non-zeroes. 60.5 • All zeroes to the right of a non-zero if the number contains a decimal.6.20, 620 • NEVER leading zeroes!0.0253, .00054 • Counting numbers and constants do not count as sig figs.

  15. Significant Figures • When adding and subtracting: Answer must have the same # of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point • Example: 28.0 23.538 +25.68 77.218 = 77.2

  16. Significant Figures • Multiplication and Division: Answer must have the same # of significant figures as the measurement with the fewest sig figs. • Example: Volume of an object with dimensions L = 3.65 cm, W= 3.20 cm, H= 2.05 cm 3.65 x 3.20 x 2.05= 23.944 cm3 How many sig figs does it need?

  17. 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.

  18. 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?

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