Download Rounding Significant Figures

UNITS OF MEASUREMENTS
1. A quantity is something that has magnitude, size, or amount.
2. In 1960 the General Conference on Weights and Measurements decided
all countries would use the International System of Units (Metric) system
as the standard units of measurements.
3. Almost every country uses the metric system for daily calculations except the
United States and Great Britain.
4. When using the metric system commas are not used with numbers because
other countries use commas to represent a decimal point.
Ex. 75, 000 is written 75 000
0.001256 is written 0.001 256
5. The metric system (SI system) is based on powers of 10.
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5. There are seven fundamental units in the metric system. All other units are
derived from these units.
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6. A derived unit is a combination of fundamental units.
Example: The unit for force is the Newton = N= kg x m / s2
Example: The unit for energy is the Joule = force x length = Nm
= kg x m2 / s2
Example: Area is calculated L x W = m x m = m2
7. If a unit is not a fundamental unit, it is a derived unit.
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8. What about volume?
Notice that liter ( the unit for volume) is not a fundamental unit.
To determine the volume of an object a length must be measured. So,
volume is derived from length.
Volume = l x w x h
=mxm xm
= m3
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11.
1 ml = 1 cm3
A 1 cm x 1 cm x 1cm cube will hold 1 ml of liquid.
1 ml = 1cm3 = 1 cc (cubic centimeter)
12. 1000 ml = 1 Liter
1000cm3 = 1 L
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12. 1000 cm3 = 1000 ml
1000 ml = 1 Liter
1000cm3 = 1 L
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Why Metric?
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1.3 Scientists Measure
Physical Quantities
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A physical quantity must include:
A NUMBER + A UNIT
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13. The metric system provides a standard unit of measurements used by all
countries. Is the man 92.5 m, 92.5 cm, 92.5 in, or 92.5 ft?
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How many centimeters are in an inch?
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UNCERNTAINTY IN MEASUREMENTS AND
SIGNIFICANT FIGURES
1. Whenever a measurement is taken, the last digit is uncertain and estimated.
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Which clock would be the most accurate?
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RULES FOR COUNTING SIGNIFICANT FIGURES
1. All nonzero digits are significant.
Ex. 123 g
3 significant figures.
25 g
2 significant figures
26.42 g 4 significant figures
2. All zeros between non zero digits are significant.
Ex. 506 L
3 significant figures
900.43 L 5 significant figures
3. Decimal numbers that begin with zero.
The zeros to the left of the first nonzero number are not significant.
Ex. 0.205 L 3 significant figures
0.0047 L 2 significant figures
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4. Decimal numbers that end in zero.
The last zero is significant.
Ex. 8.00 g
3 significant figures
35.000 g
5 significant figures
8.0 g
2 significant figures
5. Non decimal numbers that end in zero.
The zero is significant only when a written decimal is shown.
Ex. 480 g
2 significant figures
900 g
1 significant figure
90. g
2 significant figure
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PRACTICE
Determine the number of significant figures.
1. 65.42 g
2. 385 L
3. 0.14 ml
4. 709.2 m
5. 5006.12 kg
6. 400 dm
7. 260. mm
8. 0.47 cg
9. 0.0068 km
10. 7.0 cm
11. 36.00 g
12. 0.0070 kg
13. 100.6040 L
14. 340.00 cm
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Rounding Significant Figures
Sample:
205.80
0.0583
8.159
47.374
897.48
round to 3 significant figures (sf)
round to 1 sf ______
round to 3 sf ______
round to 4 sf ______
round to 2 sf ______
_______
Practice
Round to the indicated number of significant figures.
1.
2.
3.
4.
5.
6.
7.
8.
24 km to 2 sf
0.04851 L to 2 sf
2.68 g to 2 sf
4.165 L to 3 sf
2.68 g to 2 sf
8.35 ml to ml 2 sf
12 ml to 1 sf
0.06350 to 2 sf
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MULTIPLYING AND DIVIDING SIGNIFICANT FIGURES
1. The arithmetic product or quotient should be rounded off to the same number of
significant figures as in the measurement with the fewest significant figures.
???????????????????????
Keep the smallest number of significant figures.
Examples:
2.86 g x 2.0 g = 5.72 g the answer is 5.7 g
38 ml / 1.25 ml = 30.4 ml the answer is 30. ml
0.596 g x 0.3450 g = 0.20562 g the answer is 0.206 g
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Adding and Subtracting Significant Figures
1. The arithmetic result should be rounded off so that the final digit is in the same
place as the leftmost uncertain digit.
Ex. 213.67 g - 98 g = 115.67 g the answer is 116 g
3127.55 g – 784.2 g = 2343.35 g the answer is 2343.4 g
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PRACTICE
1. 9.40 cm x 2.6 cm =
____________
2. 8.08 dm x 5.3200 dm =
____________
3. 4.07 g + 1.863 g =
____________
4. 36.427 m + 12.5 m + 6.33 m
____________
5. 1.50 g / 2 cm3 =
____________
6. 0.08421 g / 0.640 ml =
____________
7. 21.50 g / 4.06 cm x 1.8 cm x 0.905 cm =
____________
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Scientific Notation
1. Convert 21300000 to scientific notation
2.13 x 10 7
2. Convert 0.0000000020 to scientific notation
2.0 x 10-9
Practice: Convert to scientific notation
1.
2.
3.
4.
5.
6.
7.
900
750000
93000000
0.000403
0.000082
0.009700
250000
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CALCULATOR PRACTICE
1. 3 x 1055 x 7.56 x 1015 =
2 x 10 71
2. 3.71 x 10 -26 x 4.00 x 10-45 =
1.48 x 10-70
Practice: Don’t forget to keep the correct number of significant figures.
1.
2.
3.
4.
5.
2.6 x 102 + 4.1 x 102
8.3 x 10-5 + 1.2 x 10-5
7.43 x 104 - 5.09 x 104
(3 x 10 5 )( 2 x 107 )
(7.5 x 106 )/(4 x 10-2)
=
=
=
=
=
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BACK TO ROUNDING SIGNIFICANT FIGURES INVOLVING
SCIENTIFIC NOTATION
1. Round 400 g to 3 significant figures.
4.00 x 102
2. Round 0.000003 to 2 significant figures
3.0 x 10-6
Simply change the number to scientific notation when going from a
smaller number of significant figures to a larger.
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IMPORTANT REMINDER:
Your calculator does not know how to do significant
figures. YOU must report numbers using the correct
number of significant figures.
If you trust the number your calculator gives you, you
might get the answer wrong!!!! TI or Casio don’t care
what grade you get on the test.
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ACCURACY AND PRECISION
1. Accuracy is the closeness of the measurements to the true or accepted
value.
2. The accuracy of an instrument can only be determined if the true or
or accepted value for the measured item is known.
3. Precision refers to the agreement among the numerical values of a set
of numbers.
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Picture 1 is accurate and precise
Picture 2 is precise but not accurate.
Picture 3 is neither accurate or precise.
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4. Scientific instruments should be accurate. If instruments are accurate,
they are also precise.
5. If an instrument is precise, it may not be accurate.
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Dimensional Analysis
(Factor Label)
1. Dimensional Analysis (factor label) is a problem solving technique.
2. This method of problem solving uses conversion factors.
3. A conversion factor is a ratio that is equal to one.
Example:
4 quarters = $1
24 hours = 1 day
185 days = 1 student school year
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Calculation Corner: Unit Conversion
1 foot
12 inches
12 inches
1 foot
“Conversion factors”
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Calculation Corner: Unit Conversion
1 foot
12 inches
12 inches
1 foot
“Conversion factors”
(
3 feet
)(
12 inches
1 foot
)
=
36 inches
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Calculation Corner: Unit Conversion
1 foot = 12 inches
1 foot
12 inches
12 inches
1 foot
=
1
=
1
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Calculation Corner: Unit Conversion
1 foot = 12 inches
1 foot
12 inches
=
1
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Calculation Corner: Unit
Conversion
1 foot = 12 inches
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Fahrenheit
Celsius
32°F
0°C
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Celsius
0°C
273K
-459
°F
-273
°C
0K
Kelvin
Fahrenheit
32°F
40
32°F
0°C
Kelvin
Fahrenheit
100
°C
Celsius
212
°F
373K
273K
0K
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