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WHERE MATH BECOMES REALITY! Measurements and Calculations

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 Calorie Cubit Foot-pound Fahrenheit

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

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

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

Refresher……

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.

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”.

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”?

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.

Scientific Notation Refresher…. The Arabic number system is based on 10! 10 1 is one decimal place, right? What about 10 -3 ? Let’s practice!

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.

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?

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

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

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 E R = E A / accepted * 100

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?

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

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