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CHEM 105
Measurements, Units, Significant Figures, Scientific Notation
Measurements:
observations that provide numerical information about a subject or topic
Contain a number and a unit
Have a degree of uncertainty
Always estimate measurements to 1 place beyond marks on a device
Use significant figures to indicate correct degree of certainty
1.
Use each of the rulers below to measure the line.
Answer:___________________________
Answer:___________________________
Significant Figures:
all of the numbers in a measurement including the estimated place
1. Number of sig figs is independent of the decimal point
2. All nonzero digits are significant
3. Leading zeros are not significant
4. Captive zeros are significant
5. Trailing zeros are significant
Sig Figs in calculations:
least sig figs or decimal places determines answer
Multiplication and division:
The final calculated answer should have the same number of sig figs as the measurement with the
fewest
sig figs
0.32 cm x 8.02 cm x 1.210 cm = 3.105344 cc
answer: 3.1 cc
2 sf
3 sf
4 sf
7 sf
2 sf
Addition and subtraction
– consider digits – indication of precision
The final calculated answer should have the same number of
digits
to the right of the decimal point as
the measurement with the least number of digits to the right of the decimal point.
5876.07 g
2 digits to the right
+
1.3045 g
4 digits to the right
5877.3745 g
4 digits to the right
answer: 5877.37 g
2 digits to the right
Rules for rounding:
applies to digit to right of sig fig digit
1. If 4 or less, drop it and all digits that follow
2. If 5 or greater, increase last significant digit by 1 and drop the rest
2.
Perform the following mathematical operations and report your answer in correct significant
figures. Assume all numbers are measurements.
a.
5.987 x 0.24 = ___________________________________________
b.
5.987 + 0.24 = ___________________________________________
c.
27.8 + 0.205 = ___________________________________________
d.
5.505 x 0.0066550 = ______________________________________
CHEM 105
Measurements, Units, Significant Figures, Scientific Notation
e.
(2.075)(0.585)
= __________________________________________
(8.42)(0.0045)
f.
25.0
= __________________________________________________
5.00
Scientific (exponential) notation:
expressing numbers as a small number multiplied by a power of 10
Rules for expressing numbers in scientific notation
1. Move the decimal point so that there is only 1 nonzero digit to the left (will be a number
between 1 and 10)
1670352
1.670352
2. The number of places you moved the decimal point is the exponent (or power) to which you
raise 10.
1670352 = 1.670352 x 10
6
moved 6 places
3. If you moved decimal point to the left, exponent is positive
(starting number was greater than 1)
4. If you moved the decimal point to the right, exponent is negative
(starting number was less than 1)
3.
Write the following measurements in scientific notation:
a.
350. g _________________________________________
b.
0.000160 L ____________________________________
c.
5,220,001 m ___________________________________
d.
0.0000008 g ___________________________________
e.
8931.5 s ______________________________________
f.
28,000.0 cm ___________________________________
4.
Change the following measurements to regular format and indicate the number of significant
figures:
a.
6.75 x 10
-5
g_____________________________________________
b.
9.904 x 10
6
dL ___________________________________________
c.
4.4420 x 10
3
mL __________________________________________
d.
7.295 x 10
-2
mm___________________________________________
e.
3 x 10
-7
L ________________________________________________
f.
2.85 x 10
2
mg ____________________________________________
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True Value
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1.
6.
Trial # 1
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Trial # 1
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Trial # 2
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765.9 atm
Trial # 1
1.44 cm
Trial # 2
765.8 atm
Trial # 2
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Trial # 3
766.4 atm
Trial # 3
1. 40 cm
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Trial # 1
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