where math becomes reality! measurements and calculations

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?

MillenniumSlugBushelKilogramCalorieCubitFoot-poundFahrenheit

Quantity Base Unit

TimeMassDistance or lengthTemperatureAmount of

substanceAmount of

electricityLight brightness

SecondKilogramMeterKelvinMoleAmpereCandela

Only 7 quantities can be measured directly!

...everything else is calculated!

SpeedCurrentEnergyVolumeWeightForce

…Which we call “derived” units…

What do you think “modified” units might be?

“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?

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 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

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!101 is one decimal place, right?What about 10-3?

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

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.

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

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?

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?