The document discusses key concepts in scientific measurement including: 1) Distinguishing between quantitative and qualitative measurements and listing common SI units and prefixes. 2) Distinguishing between mass and weight and discussing density. 3) Converting units and identifying significant figures in measurements and calculations. 4) Discussing accuracy, precision, and errors in measurement.

1. Scientific Measurement

2. Scientific
Measurement
 Distinguish between quantitative and qualitative measurements.
 List SI units of measurement and common SI prefixes.
 Distinguish between the mass and weight of an object.
 Convert measurement to scientific notation.
 Distinguish among the accuracy, precision, and error of
measurement.
 Identify the number of significant figures in a measurement and in the
result of calculation.
 Identify and calculate derived units.
 Calculate the density of an object from experiment data.
TEKS: 2A, 2B, 2C, 2D, 2E, 3C, 3D, 3E, 4B, 4C

3. Quantitative vs. Qualitative
Observations
 Qualitative – observations made with
adjectives
“The water is clear and cool.”
 Quantitative – observations that include a
measurement or other numeric data
“There are 40mL of water.”

4. Two parts of measurements
1. Quantity – indicates size or
magnitude (how much?)
2. Unit – tells us what is to be measured
and compares it to a previously defined
size (of what?)
Measurements must have both
a quantity and a unit to be valid.

5. International System of Units
 Length – meter
 Mass – kilogram
 Temperature – Kelvin
 Energy – joule
 Amount of a substance – mole
 Electric current - ampere
 Volume – m3
 Density – g/cm3
 Weight - Newton

6. Commonly Used Prefixes in the Metric
System
Prefix Meaning Exponent
mega (M) 1 000 000 106
kilo (k) 1000 103
hecto (h) 100 102
deka (da) 10 101
deci (d) 1/10 10-1
centi (c) 1/100 10-2
milli (m) 1/1000 10-3
micro (µ) 1/1 000 000 10-6
nano (n) 1/1 000 000 000 10-9
pico (p) 1/1 000 000 000 000 10-12

7. Conversion Factors
 Conversion factors are equalities written in ratio form:
1 km = 1000m 1km = 1000 m
1000 m 1 km
 Choose the format that allows you to cancel the
original units and leave the new units.
Ex. 2.5 km = ________ m
You would choose 1000 m
km

8. Conversion Factors
 Make sure that you have a valid equality
before writing your conversion factor.
Which of these equalities are correct?
1 m = 1 x 10-6 µm
1 m = 1 x 106 µm
1 x 10-6 m = 1µm

9. 1 dm Important Equalities
10 cm
1 dm 1 dm3 = 1000cm3
10 cm
1mL = 1cm3 = 1cc
1dm3 = 1000 mL = 1L
100 dm3 = ‗‗‗‗nm3

10. Conversion Practice
 Problem
List in order – largest to smallest
a. 1 dm3
b. 1 µL
c. 1 mL
d. 1 L
e. 1 cL
f. 1 dL

11. Derived Units
 Derived units are formed from a
combination of other units.
 Examples include:
m/s & km/hr (speed), cm3 & dm3(volume),
J/g· C (specific heat), g/mol (molar mass),
g/cm3 & kg/m3 (density)

12. Density
 Density is the ratio between the mass and
volume of an object.
 Density = Mass or D=m
Volume V
 Density is an intensive physical property.

13. Density Problems
A student finds a shiny piece of metal that she
thinks is aluminum. She determined that the
metal has a volume of 245 cm3 and a mass of
612 g. Calculate the density. Is the metal
aluminum?
The density of silver at 20ºC is 10.5 g/cm3.
What is the volume of a 68 g bar of silver?

14. Density Problems Continued
 A weather balloon is inflated to a volume of 2.2 x
103 L with 37.4 g of helium. What is the density
of helium, in grams per liter.
 A plastic ball with a volume of 19.7 cm3 has a
mass of 15.8 g. What is its density? Would the
ball sink or float in a container of water?

15. Specific Gravity
Specific Gravity = Density substance (g/cm3)
Density water (g/cm3)

16. Making Measurements

17. Precision and Accuracy
 Accuracy refers to the agreement of a
particular value with the true value.
(how close)
 Precision refers to the degree of agreement
among several elements of the same
quantity. (how repeatable)

18.  Target (a) shows
neither accuracy or
precision.
 Target (b) shows
precision, but not
accuracy.
 Target (c) shows both
accuracy and
precision.

19. Uncertainty in Measurement
 A digit that must be estimated is called
uncertain.
 The last digit in a measurement always
shows uncertainty.

20. Significant Digits
 Significant Digits show the degree of
certainty in a measurement.
 Not all digits in a number show certainty,
therefore, all digits are not significant.

21. Counting Significant Digits
Rule 1:
 Nonzero integers always count as significant
digits.
 3456 has 4 “sig digs”

22. Counting Significant Digits
Rule 2:
 Leading zeros do not count as significant
figures.
 0.0486 has 3 “sig figs”

23. Counting Significant Digits
Rule 3:
 Captive zeros always count as significant
figures.
 16.07 has 4 “sig digs”

24. Counting Significant Digits
Rule 4:
 Trailing zeros are significant only if the number
contains a decimal point.
 9.300 has 4 “sig figs”

25. Counting Significant Digits
 Exact numbers have an infinite number of
significant figures.
 Exact numbers include counting numbers
and conversion factors.
 Examples:
 12 students
 1m = 100 cm

26. Practice Problems
 Determine the number of significant figures.
a. 12 kilometers
b. 0.010 m2
c. 507 thumbtacks
d. 0.070020 m
e. 10800 m
f. 5.00 m3.
g. 2.340 x 103 cm
h. 6.02 x 1023 atoms

27. Rules for Significant Figures in
Mathematical Operations
 Multiplication and Division: # sig figs in the
result equals the number in the least precise
measurement used in the calculation.
 6.38 cm 2.0 cm = 12.76 cm2
 13 (2 sig figs)

28. Multiplication and Division
 Your answer can only have the least number of
significant figures in your data.
a.
2.0 mL
x 3.00 mL
b.
8432 m =
12.5 m

29. Rules for Significant Figures in
Mathematical Operations
 Addition and Subtraction: # sig figs in the result
equals the number of decimal places in the least
precise measurement.
 6.8 cm + 11.934 cm + 3.7556 cm = 22.4896 cm
 22.5 cm (1 digit after decimal - 3 sig figs)

30. Addition and Subtraction
Count the decimal places. You can only have in
your answer the least number of decimal places
that is seen in your data.
1.0 1 7.00 1
1.00 + 2.00 - 1.001 + 0.5
+ 1.000

31. Rounding Rules
If the digit following Then the last digit Example (rounded to 3
the last digit to be should: sig dig’s)
retained is:
greater than 5 be increased by 1 38.68 g to 38.7 g
less than 5 stay the same 12.51 m to 12.5 m
5, followed by nonzero be increased by 1 4.8851 cm to 4.89 cm
digit(s)
5, not followed by be increased by 1 2.975 kg to 2.98 kg
nonzero digit(s), and (because 7 is odd)
preceded by an odd digit
5, not followed by Stay the same 2.985 kg to 2.98 kg
nonzero digit(s), and the (because 8 is even)
preceding significant
digit is even

32. Measurement Tips

33. Measurement Tools
•Distance = Meter Sticks & Metric Tapes
•Volume = Graduated Cylinder
•Time = Stopwatch
•Mass = Balance
•Weight = Spring Scale

34. Mass vs. Weight
 Mass is the amount of matter in an object;
weight is the effect of gravity on a mass.
 Mass is measured on a balance; weight is
measured with a scale.
 Mass remains constant at all locations;
weight varies with change in gravitational pull.

35. Volume
1. Never measure in a beaker. They are
for estimation only!
2. Place the graduated cylinder on a
level surface and read the bottom of
the meniscus.
3. Check the scale of the graduated cylinder.
Different scales for different sizes!
4. Use displacement to find the volume
of irregular solids.

36. Mass
1. Make sure the balance is on a level
surface.
2. Use the same balance in the same
place for all parts of a procedure.
3. DO NOT MOVE A BALANCE ONCE IT IS ZEROED!

37. Length
 Rulers & meter sticks wear on the ends – start at
a point other than zero.
 Choose the unit most reasonable for the item
you are measuring – make sure you convert
your number accordingly.