The Fundamental Tools

Of Science

Units

• Some fundamental measurements in all of science:

• Length• Time• Mass

• Many others are combinations of these:• Energy, Speed, Volume, Area

Units

• International Standard Units (SI, aka metric)– Length (m – meter)– Mass (kg – kilogram)– Time (s – seconds)– Energy (J – joules)– Temperature (K – kelvin)

Temperature ScalesTemperature Scales

Notice that 1 kelvin degree = 1 degree Celsius1 kelvin degree = 1 degree Celsius

Boiling point Boiling point of waterof water

Freezing point Freezing point of waterof water

CelsiusCelsius

100 ˚C100 ˚C

0 ˚C0 ˚C

100˚C100˚C

KelvinKelvin

373 K373 K

273 K273 K

100 K100 K

FahrenheitFahrenheit

32 ˚F32 ˚F

212 ˚F212 ˚F

180˚F180˚F

Temperature Temperature ScalesScales

100 100 ooFF38 38 ooCC311 K311 K

oF oC K

Significant Figures:

Digits in a measurement having values that are known with certainty plus one digit having a value that is estimated.

Reading Volume: Significant Figures on an Instrument

• Measurements that contain a greater number of significant figures are more precise than measurements that contain fewer significant figures.

• Always select an instrument that gives you the most significant figures. Only

report as many sig figs as that

instrument allows

The Rules

All numbers 1-9 are significant.Zeros are sometimes significant, here's how

you can tell: If a decimal point is present, starts on the

Pacific side, move across until you get to a 1-9 digit, and start counting to the end

If a decimal point is absent, start on the Atlantic side, move across until you get to a 1-9 digit, and start counting to the end

1005 contains ? sig. Figs., 23,000 has ?, 1,045,090 has ?

40.01 has ?1.100 has ? sig figs, 0.00540 has ?,

When multiplying or dividing measurements: round the answer to the same number of digits as the measurement having the fewest number of significant figures.

When adding or subtracting measurements: round the answer to the same number of decimal places as the measurement having the fewest number of decimal places.

• Identify the LEAST PRECISE measurement.

• Identify the MOST PRECISE digit (place) within that measurement.

• Round the answer to this digit (place).

123456.7890

Higher precision

Lower precision

Conversion

• Commonly Used Prefixes:– kilo = 1000 of something ( 1km= 1000m, kg)– deci =0.1 of something (10 dm = 1m)– centi = 0.01 of something (100 cm = 1m)– milli = 0.001 of something (103 mm = 1m)– micro = 0.000001 (106 µm = 1m)– nano = 0.000000001 (109 nm = 1m)– pico = 0.000000000001 (1012 pm = 1m)

Refer to Conversion Chart to additional prefixes

• All conversion factors are fractions.

Conversion

100 cm 100 cm

1 m 100 cm

1m

10-6 µm

= = 1

= = 1 1m

10-6 µm

1 km

103 m= = 1

103 m

103 m

• Units are multiplied and divided like numbers are.

The Nature of Units

10 meters

2 meters = 5 (the units cancel out)

50 miles

10 gallons = 5 miles/gallon (the units combine as a fraction)

10 meters x 10 meters x 10 meters = 103 m3

(the units combine as exponents)

•Only IDENTICAL UNITS on 2 numbers can be added or subtracted.

•The answer always has the same units.

100 kg – 25 kg = 75 kg

100 kg – 25 m = Meaningless Dribble

How many seconds are in 54 days?

• Write the measurement with its unit.

• If it isn’t already a fraction, write it over 1.

• Set up conversion factors that– Cancel units you want to get rid of– Replace with units you are looking for– Have values on the top and bottom that are

equivalent

• Multiply numbers across the top

• Multiply numbers across the bottom

• Divide to get answer, check units

Scientific Notation• 10000000000000000000000• 0.00000000000000000000000000001

• There has to be a better way to write those numbers

• Rules for scientific notation– 1) Always express the number starting with the one’s place

followed by any decimal digits, times a power of 10.– 2)To express a large number, count the number of decimal

places needed to move to the one’splace, and make that number the exponent of ten.

– 3) To express a very small number, count the number of decimal places needed to move to the one’s place, and make that number the NEGATIVE exponent of ten.

– 4) After re-expressing the number in scientific notation, check it by writing out the expanded ten, and multiply it by the measured number.

Scientific Notation

• Examples:0.000000000000000000000000000000001

= 1.0 x 10-35

94140000000000000000000000000000000

= 9.414 x 1035

20

Accuracy – how close a measurement is to the true value

Precision – how close a set of measurements are to each other

accurate&

precise

precisebut

not accurate

not accurate&

not precise

Precise if they give many significant digits

Accurate if calibrated to a standard

To report the accuracy of your measurements

Observed – True True

X 100

To report the precision of your measurements

1

2

3

Average your measurements

Find the absolute values of the differences between each measurement and the average

Average these differences