the fundamental tools
DESCRIPTION
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) - PowerPoint PPT PresentationTRANSCRIPT
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