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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 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?

Refresher……

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 Student AStudent BStudent C Trial 11.54 g/mL1.40 g/mL1.70 g/mL Trial 21.60 g/mL1.68 g/mL1.69 g/mL Trial 31.57 g/mL1.45 g/mL1.71 g/mL Average1.57 g/mL1.51 g/mL1.70 g/mL

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”?

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

Scientific Notation Two factors: 1. A number between 1 and 10 2. 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 10 6 0.000000028 – 2.8 x 10 -8

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.

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

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 cm 3 How m any sig figs does it need?

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?

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