1. The Fundamental Tools
Of Science

2. Units Some fundamental measurements in all of science:
Length
Time
Mass
Many others are combinations of these:
Energy, Speed, Volume, Area
*THINK: What does it mean to be a combined unit?

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

4. Temperature Scales Fahrenheit Celsius Kelvin 32 ˚F 212 ˚F 180˚F 100 ˚C
Boiling point of water
32 ˚F
212 ˚F
180˚F
100 ˚C
0 ˚C
100˚C
373 K
273 K
100 K
Freezing point of water
Notice that 1 kelvin degree = 1 degree Celsius

5. Temperature Scales
100 oF
38 oC
311 K oF oC K

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

7. Reading Volume: Significant Figures on an Instrument
Record the digits you know for sure, then estimate one place. What do you get for these two measurements?

8. 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

9. The Rules
ATLANTIC
PACIFIC

10. 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
1.100 has ? sig figs, has ?,
40.01 has ?
1005 contains ? sig. Figs., 23,000 has ?, 1,045,090 has ?

11. 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 place value of the measurement with the least significant place value.

12. 123456.7890 Identify the LEAST PRECISE measurement.
Higher precision
Lower precision
Identify the LEAST PRECISE measurement.
Identify the MOST PRECISE digit (place) within that measurement.
Round the answer to this digit (place).

13. 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 = of something (103 mm = 1m)
micro = (106 µm = 1m)
nano = (109 nm = 1m)
pico = (1012 pm = 1m)
Refer to Conversion Chart to additional prefixes

14. Conversion = = 1 = = 1 All conversion factors are fractions. =
100 cm cm
1 m cm =
= 1
The top and bottom of a conversion factor must equal each other.
1 km
103 m
103 m
= 1 =
Therefore, every conversion factor must equal 1. 1m
10-6 µm
10-6 µm =
= 1
When you multiply a measurement by 1 you do not change its value!

15. 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

16. 54 days . 24 hours . 60 mins . 60 secs = 1 1 day 1 hour 1 min
This is how you set up the conversions for the problem
on the previous slide:
54 days . 24 hours . 60 mins . 60 secs =
day hour min
To solve, check that units cancel and leave you with the unit you want. Then, multiply across the top, multiply across the bottom, then divide your answers.

17. Try a few more… 2 m = ____ cm 34.5 mm = ____ m
24 in = _____ m (Hint: sometimes we need more than one conversion factor!)
OH WOW THIS LOOKS HARD!!!
15.0 miles = _______ ft
hour sec
Conversions you don’t need to memorize:
5280 ft = 1 miles
3 feet = 1 yard
12 in = 1 ft
2.54 cm = 1 in
(Hint: units on the bottom can be changed, too! Also, per hour means 1 hour and per sec means 1 sec….)

18. The Nature of Units Units are multiplied and divided like numbers are.
10 meters
2 meters
= (the units cancel out)
10 meters x 10 meters x 10 meters = 103 m3 (the units combine as exponents)
50 miles
10 gallons
= 5 miles/gallon (the units combine as a fraction)
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

19. Scientific Notation
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.

20. Scientific Notation Examples: 0.0000000000000000000000000000000010
= x 1035
Scientific notation is a great way to display significant digits: The significant digits appear before the x10 in Scientific Notation!

21. More About Unit Conversions
Sometimes we need to convert squared or cubed units…. IT’s EASY! Just square or cube the conversion factor. Convert 0.62 m2 to cm2 = 6200 cm2

22. Accuracy Precision
What's the difference??

23. Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise

24. Instruments are...
Precise if they give many significant digits
Accurate if calibrated to a standard

25. Observed – True X 100 True Percent Error
To report the accuracy of your measurements
Observed – True
True
X 100

26. To report the precision of your measurements
Average Deviation
To report the precision of your measurements 1
Average your measurements 2
Find the absolute values of the differences between each measurement and the average 3
Average these differences