where math becomes reality! measurements and calculations

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WHERE MATH BECOMES REALITY! Measurements and Calculations

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Page 1: WHERE MATH BECOMES REALITY! Measurements and Calculations

WHERE MATH BECOMES REALITY!

Measurements and Calculations

Page 2: 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.

Page 3: WHERE MATH BECOMES REALITY! Measurements and Calculations

Do you recognize any of these units?

MillenniumSlugBushelKilogramCalorieCubitFoot-poundFahrenheit

Page 4: WHERE MATH BECOMES REALITY! Measurements and Calculations

Quantity Base Unit

TimeMassDistance or lengthTemperatureAmount of

substanceAmount of

electricityLight brightness

SecondKilogramMeterKelvinMoleAmpereCandela

Only 7 quantities can be measured directly!

Page 5: WHERE MATH BECOMES REALITY! Measurements and Calculations

...everything else is calculated!

SpeedCurrentEnergyVolumeWeightForce

…Which we call “derived” units…

What do you think “modified” units might be?

Page 6: WHERE MATH BECOMES REALITY! Measurements and Calculations

“metric” system

Actually, called “SI” for systeme internationala worldwide agreement among scientists to

adopt this method of measurement.Also called, “kg-m-s” system for

Kilogram Meter Second

Should US officially adopt?

Page 7: WHERE MATH BECOMES REALITY! Measurements and Calculations

Refresher……

Page 8: WHERE MATH BECOMES REALITY! Measurements and Calculations

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 A Student B Student C

Trial 1 1.54 g/mL 1.40 g/mL 1.70 g/mL

Trial 2 1.60 g/mL 1.68 g/mL 1.69 g/mL

Trial 3 1.57 g/mL 1.45 g/mL 1.71 g/mL

Average 1.57 g/mL 1.51 g/mL 1.70 g/mL

Page 9: WHERE MATH BECOMES REALITY! Measurements and Calculations

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.

Page 10: WHERE MATH BECOMES REALITY! Measurements and Calculations

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”.

Page 11: WHERE MATH BECOMES REALITY! Measurements and Calculations

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”?

Page 12: WHERE MATH BECOMES REALITY! Measurements and Calculations

Scientific Notation Refresher….

The Arabic number system is based on 10!101 is one decimal place, right?What about 10-3?

Page 13: WHERE MATH BECOMES REALITY! Measurements and Calculations

Scientific Notation

Two factors:1. A number between 1 and 102. 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

Page 14: WHERE MATH BECOMES REALITY! Measurements and Calculations

Which numbers are significant?

All non-zeroes. 72.3Zeroes between non-zeroes. 60.5All zeroes to the right of a non-zero if the

number contains a decimal. 6.20, 620NEVER leading zeroes! 0.0253, .00054Counting numbers and constants do not

count as sig figs.

Page 15: WHERE MATH BECOMES REALITY! Measurements and Calculations

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: 28.023.538

+25.68 77.218 = 77.2

Page 16: WHERE MATH BECOMES REALITY! Measurements and Calculations

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 cm3.65 x 3.20 x 2.05= 23.944 cm3

How many sig figs does it need?

Page 17: WHERE MATH BECOMES REALITY! Measurements and Calculations

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.

Page 18: WHERE MATH BECOMES REALITY! Measurements and Calculations

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?