Significant Figures -why we use them -rules for sig. figs. -operations with sig. figs.
CHEMISTRY - 3.1 Accuracy Precision Practice Sig Figs and Sci Notation
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Transcript of CHEMISTRY - 3.1 Accuracy Precision Practice Sig Figs and Sci Notation
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Standards for Measurement
Lesson 3.1, Continued… Accuracy & Precision Significant Figures Scientific Notation
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Accuracy & Precision
Precision: How closely individual measurements compare
with each other The “fineness” of a measurement
Accuracy: how closely individual measurements compare with the true or accepted value
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Accurate or Precise?
Precise!(but not accurate)
What is the temperature at which water boils?
•Measurements: 95.0°C, 95.1°C, 95.3°C
•True value: 100°C
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Accurate or Precise?
Accurate!(it’s hard to be accurate without being precise)
What is the temperature at which water freezes?
•Measurements: 1.0°C, 1.2°C, -5.0°C
•True value: 0.0°C
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Accurate or Precise?
Not Accurate & Not Precise(don’t quit your day job)
What is the atmospheric pressure at sea level?
•Measurements: 10.01 atm, 0.25 atm, 234.5 atm
•True value: 1.00 atm
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Accurate or Precise?
Accurate & Precise(it’s time to go pro)
What is the mass of one Liter of water?
•Measurements: 1.000 kg, 0.999 kg, 1.002 kg
•True value: 1.000 kg
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Significant figures (“sig figs”): the digits in a measurement that are reliable (or precise). The greater the number of sig figs, the more precise that measurement is.
A more precise instrument will give more sig figs in its measurements.
Significant Figures
Every measurement has some degree of uncertainty.
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Uncertainty examples: To measure the time for a pencil to fall…
compare a stopwatch and a wall clock.
To measure the volume of a liquid…compare a graduated cylinder and a beaker.
The stopwatch & graduated cylinder are more precise instruments…so the readings
they produce will have more sig figs.
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A graduated cylinder:
50
100 mL Beaker
50 mL Graduated cylinder
A beaker:
41.0
41.2 mL (3 sig figs = very precise)
40. mL (2 sig figs = not as precise)
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When are digits “significant”?
“PACIFIC”
Decimal point is PRESENT. Count digits from left side, starting with the first nonzero digit.
The “Atlantic-Pacific” Rule
40603.23 ft2
0.01586 mL
= 7 sig figs
= 4 sig figs
PACIFIC
PACIFIC
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When are digits “significant”?
“ATLANTIC”
Decimal point is ABSENT. Count digits
from right side, starting with
the first nonzero digit.
40600 ft2
1000 mL
3 sig figs =
1 sig fig =
ATLANTIC
ATLANTIC
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0.00932Decimal point present → “Pacific” → count digits from
left, starting with first nonzero digit= 3 sig figs
4035Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs
27510Decimal point absent → “Atlantic” → count digits from right, starting with first nonzero digit= 4 sig figs
Examples
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Scientific Notation
“Writing a number as a power of 10.”
Why? It makes very large and very small numbers more manageable to write and use. Rule of thumb: Use when number is greater than 100
or smaller than 0.10. Or, you may always use it!
The number of sig figs are clearly shown in a measurement.
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2.4: Scientific Notation
How important is a change in the power of 10?
Diameter of Earth’s orbit around the sun
≈ 100,000,000,000 m = 1.0*1011 m
Diameter of an atom
≈ 0.0000000001 = 1.0*10-10 m
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1. Move the decimal point in the original number so that it is located to the right of the first nonzero digit.
2. Multiply the new number by 10 raised to the proper power that is equal to the number of places the decimal moved.
3. If the decimal point moves: To the left, the power of 10 is positive. To the right, the power of 10 is negative.
Writing in scientific notation
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Write the following measurements in scientific notation, then record the number of sig figs.
1. 789 g2. 96,875 mL3. 0.0000133 J4. 8.915 atm5. 0.94°C
7.89*102 g9.6875*104 mL
1.33*10-5 J8.915 atm9.4*10-1 °C
3 sig figs5 sig figs3 sig figs4 sig figs2 sig figs
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Requirements for this class:
Write answers using 3 significant figures
Use scientific notation for all numbers greater than 1000 and smaller
than 0.001
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Accuracy or Precision?
When deciding on accuracy, precision, both, or neither….it is quantitative data (numerical), not qualitative
(descriptive)
1) The recipe calls for 25 chocolate chips per cookie. The cookies analyzed have 34, 35, and 32 respectively.
2) The percent NaCl is 99%, 99%, and 98%.
3) The number of grams of KF required is 0.04 g. The amounts used were 0.038, 0.039, 0.041, and 0.040.
4) To win, Henry must earn 500 points. In his three trials, he earned 400, 480, and 395 points.
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Rounding
Look at digit following specified rounding value. If it is 5 or greater, then round up. If not, truncate (cut off the rest of
the numbers).
Round to the nearest tenth 6.7512 6.7777 6.7499 6.9521
6.86.86.77.07.0
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Practice Problems p. 39-40
12. State the abbreviation for each of the following units:
a) milligramb) kilogramc) meterd) nanometere) angstromf) microliter16. State the number of
significant figures in each of the following numbers:
a) 40.0b) 0.081c) 129,042d) 4.090 x 10-3
18. Round each of the following numbers to three significant figures:
a) 8.8726
b) 21.25
c) 129.509
d) 1.995 x 106
20. Write each of the following numbers in exponential (scientific) notation:
a) 0.0456
b) 4082.2
c) 40.30
d) 12,000,000
mg
kg
m
nm
AL
3
2
6
4
8.87
21.3
130. or 1.30 x 102
2.00 x 106
4.56 x 10-2
4.08 x 103
4.03 x 101
1.20 x 107