Accurate measurements are needed for
a valid experiment.
Measurement Systems
 A. English System- pounds, ounces, feet, inches, miles,
degrees Fahrenheit, gallons, cups, teaspoons,
tablespoons.
 Metrics System- based on 10’s. Easy to convert bc all
you have to do is move your decimal.
 Measurements depend on STANDARDS—what we use
for comparison.
 Ex. Feet, meters, cubits, etc.
Quantity
length
mass
Volume (liquid)
Volume (regular)
Volume (irregular)
Definition
Unit
tool
Accuracy and Precision
Measurements should be both
accurate and precise.
Accuracy- how close a value is
to the true value
Precision- Getting the same
result after repeated trials.
Percent Error
 Percent error= (experimental value – accepted value)

accepted value
 Experimental= what you got in the lab.
 Accepted=correct or true value ;
 the value in the CRC handbook of chemistry and
physics.
 Sometimes this is the value you get from calculations.
Example
A student measures the mass and volume of a substance
and calculates its density as 1.40 g/mL. The correct, or
accepted, value of the density is 1.30 g/mL. What is the
percentage error of the student’s measurement?
Significant Figures
 In a measurement all of the digits are
known with certainty plus one final
digit, which is estimated.
 Always make your measurements as
accurate as possible, estimating the
final digit.
Rules for determining significant
figures.
Rule
Example
1. All numbers 1-9 are significant.
2. 47, 324, 34.229
2. Zeros in between non-zero numbers
are always significant.
1002
12.0009
3. Zeros at the end of a number to the
RIGHT of a DECIMAL are significant
85.000 ;
9.0000000 (zeros ARE significant)
4. Zeros in FRONT of nonzero numbers 0.0997653 (zeros are NOT significant)
are NOT significant
5. Zeros at the END of a number when
46,000 (zeros are NOT significant)
there is NOT a decimal are NOT
46,000. (decimal indicates that zeros
significant. A decimal point placed after are significant)
zeros indicates that they are significant
and are due to exact measurements.
Multiplying and Dividing
 The answer can have no more significant figures than
are in the measurement with the FEWEST number of
significant figures.
 1). Carry out the mathematical operation.
 2.) Count the number of significant figures in each
part of the problem.
 3). The answer should be rounded to have the same
number of significant figures as the smallest number
of sig figures in the problem.
Examples:
 35000 X 0.023 =
 1233 X 21.4 =
 0.0122 X 3 =
Adding and Subtracting
 When adding and subtracting decimals, the answer
must have the same number of significant figures to
the right of the decimal point as there are in the
measurement having the FEWEST digits to the right of
the decimal.
 Example: 1.2234 + 2.3 = 3.5
 When working with whole numbers, the answer
should be rounded so that the final significant digit is
in the same place as the leftmost uncertain digit.
 Example: 5400 + 365 = 5800.
Scientific Notation
 Numbers are written in the form M X 10n, where M is a
number greater than or equal to 1 and less than 10 and
n is a whole number.
 1. Determine M by moving the decimal point to the left
or right so only 1 nonzero number is to the left of the
decimal.
 2. Count the number of places that you moved the
decimal. If you moved to the left, n is positive. If you
moved to the right, n is negative.
Expand and Contract Examples.
 Put in scientific notation (contract):
 136,000
 .001234
 0.2342
 134789
 Expand the following:
 1.2 X 10-3
 9.08 X 10-8
 8.54 x 106
Put the following in correct
scientific notation.
 72.56 X 109
 0.0123 X 103
 3234.556 X 10-6
 2345 X 10-5
 0.0012234 X10-9
 0.00001345 X 108
Multiply and Divide
 Multiplying
 1. The “M’s” are multiplied.
 2. Exponents are added.
 Example: (3.4 X 105)(4.5 X 106)
 (3.4)(4.5)= 15.3 X 1011 or 1.5 X 1012
 Dividing
 1. The “M’s” are divided.
 2. Exponents are subtracted.
 Example 6.7 X 1012 / 3.4 X 106

1.97 X 106 or 2.0 x 106
Remember sig figs for multiplying
and dividing---least # sig figs in
problem…….Practice these.
 6.0 X 105/2.0 X 104=
 (3.2 X 106)(2.5 X 102)=
 (1.345 X 10-7)(3.2 X 10-1)=
 4.65 X 10-9 / 3.2 X 102=
Add and Subtract with exponents
 These operations can only be performed if the values
have the SAME EXPONENT. If they do not, adjust the
values so the exponents are equal, then just add or
subtract M and the exponent stays the same.
 Remember sig figs (#’s past the decimal)
 Example:
 Example:


(5.6 X 102) + (3.3 x 102) = 8.9 x 102
(4.2 X 103) + (6.2 X 105) =
.042 X 105 + 6.2 x 105 = 6.242 x 105
6.2 x 105
Practice—adding and subtracting
with exponents.
 1. (1.54 x 10-2) + (2.86 x 10-1) =
 2. (7.023 x 109) + (6.62 x 107)=
 3. (5.4 x 10-9) + (4.6 x 10-9) =
Quantitative vs. Qualitative
 Quantitative-measurement using numbers.
 130 meters, wavelength of 786 nm, 14.5 kg
 Qualitative-measurement not using numbers.
 Red, happy, big, far, angry
Quantitative or Qualitative??










1. The cup had a mass of 454 grams.
2. The temperature outside is 25o C.
3. It is warm outside.
4. The tree is 10 meters tall.
5. The building has 25 stories.
6. The building is taller than the trees.
7. The sidewalk is long.
8. The sidewalk is 100 meters long.
9. The race was over quickly.
10. The race was over in 10 minutes
Absolute zero
 Absolute zero is the coldest possible temperature. It is
the temperature where there is no molecular motion at
all.
 Absolute zero is 0 kelvin, or -2730C.
Temperature Conversions
 0F = (1.8 X 0C) + 32 =
 0C= 5/9 (0F - 32) =
 K= 0C + 273 =
 0C= K – 273 =
Density
Density=Mass/Volume
Mass grams, kg, mg
Volume l or ml (graduated
cylinder)
3
3
Volume m or cm (l x w x h)
Mass (unit is always in grams)
 If it is a solid, measure directly on the triple beam
balance. Remember, chemicals are never put directly
on the pan.
 If it is a liquid, first measure the mass of the empty
graduated cylinder. Then put the liquid in. Measure
the mass again. Subtract.
 Liquid and graduated cylinder
 -empty graduated cylinder
 =mass of liquid.
Volume
 If liquid-measure directly with graduated cylinder.
 Unit = mL
 If regular shaped object: Length X width X height.
 Unit = cm3
 If irregular shaped object: Put water into the
graduated cylinder (not the volume), place the object
into the water (careful not to splash), again note the
volume. Subtract. (volume with object minus volume
without object = volume of object.
 Unit = mL
Dimensional Analysis
 The process of using unit multipliers or conversion
factors to solve problems.
 Unit multipliers (conversion factors) are fractions that
equal one AND include a unit of measure, such as
meter, inch, gram, liter, etc.
 How do you use dimensional analysis most every day?
Some things to remember.
 Units are VERY important: $50 vs. 50 cents; He hit that
ball 500; get pulled over and officer says you are going
105 (105 km/hr is 65 mi/hr); You must always include
the unit.
 Units will be treated just like numbers, they will
multiply, divide, and if the units don’t cancel out like
you need them to, you know you set your problem up
wrong.
What are some examples of
conversion factors?
What are the steps?
 1. What is being asked?
 2.Start with what is given.
 3. Determine what conversions are needed.
 4. Set up problem.
 Given (Conversion) = Answer
 5. Solve.
 6. Check answer by re-cancelling units.