Transcript CH 2: Scientific Measurement

CH 2: Scientific Measurement
Renee Y. Becker
CHM 1025
Valencia Community College
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Measurements
• Measurement
– A number with an attached unit
Examples: 15 inches
3 cups
36 cm
Every measurement must include units!!
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Example 1: Measurements
In the following, what are the measurements
and what are the units?
a) 12 trees
b) 2.3 mm
c) 100 ¢
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Measurements
• Instrument
– A device for recording a measurement
• Examples: Ruler (length), electronic balance (mass),
Graduated cylinder (volume)
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Uncertainty
• An instrument may give a very sensitive
reading, but EVERY measurement has
UNCERTAINTY
• No measurement instrument is perfect and
neither is the person using it
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Example 2: Length Measurements
• If we need to measure the length of this
candycane, which ruler should we use? Why?
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Mass
• Mass
– Measure of the amount of matter it possesses
– Measured by a balance
– Not affected by gravity
– Typical units: kilogram (kg), gram (g), pound (lb),
ounce (oz)
• Weight
– Force exerted by gravity on an object
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Balances
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Example 3: Mass
• Would you have the same mass on the moon
as on Earth? Why?
• Would you have the same weight on the
moon as on Earth? Why?
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Volume
• Volume
– The amount of space occupied by a solid, gas, or
liquid
– Graduated cylinder, pipet, buret, volumetric flask,
syringe
– Typical units: milliliter (mL), Liter (L), centimeter
cubed (cm3), quart (qt), gallon (gal),
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Buret
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Accuracy, Precision, and Significant Figures in Measurement
• Accuracy is how close
to the true value a
given measurement is.
• Precision is how well a
number of independent
measurements agree
with one another.
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Accuracy, Precision, and Significant Figures in Measurement
• Significant Figures are the total number of digits
in the measurement.
• The results of calculations are only as reliable as
the least precise measurement!!
• Rules exist to govern the use of significant figures
after the measurements have been made.
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Accuracy, Precision, and Significant Figures in Measurement
• Rules for Significant Figures:
– Zeros in the middle of a number are significant
– Zeros at the beginning of a number are not
significant
– Zeros at the end of a number and following a
period are significant
– Zeros at the end of a number and before a period
may or may not be significant.
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Example 4: Significant Figures
How many Sig. Figs ?
a) 0.000459
b) 12.36
c) 36,450
d) 8.005
e) 28.050
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Accuracy, Precision, and Significant Figures in Measurement
• Rules for Calculating Numbers:
– During multiplication or division, the answer
can’t have more sig figs than any of the original
numbers.
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Example 5: Significant Figures
a) 238.5 x 79 =
b) 12 / 0.1272 =
c) 0.2895 x 0.29 =
d) 32.567 / 22.98 =
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Accuracy, Precision, and Significant Figures in Measurement
-During addition or subtraction, the answer can’t
have more digits to the right of the decimal point
than any of the original numbers.
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Example 6: Significant Figures
a) 238.5 + 79 =
b) 12.3 - 0.1272 =
c) 0.2895 + 0.29 =
d) 32.567 - 22.98 =
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Accuracy, Precision, and Significant Figures in Measurement
• Rules for Rounding Numbers:
– If the first digit removed is less than 5 - round down
– If the first digit removed is greater than 5 - round up
– If the first digit removed is 5 and following numbers are
nonzero - round up
– If the first digit removed is 5 and following numbers are
zero - round down
– Only final answers are rounded off, do not round
intermediate calculations
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Example 7: Rounding
Round off each of the following measurements
(a) 3.774499 L to four significant figures
(b) 255.0974 K to three significant figures
(c) 55.265 kg to four significant figures
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Example 8: Accuracy & Precision
Which of the following is precise but not accurate?
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Scientific Notation
• Changing numbers into scientific notation
– Large # to small #
– Moving decimal place to left, positive exponent
123,987 = 1.23987 x 105
– Small # to large #
– Moving decimal place to right, negative
exponent
0.000239 = 2.39 x 10-4
• Correct scientific notation:
#.#### x 10n
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Scientific Notation
How to put into calculator??
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Example 9: Scientific Notation
Put into or take out of scientific notation
a) 87542
b) 2.1956 x 10-3
c)
0.784
d) 2.78 x 106
e) 92000
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Significant Figures
• When we count something, it is an exact
number.
– It has an infinte number of significant figures
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