sig figs. scientific notation in science, we often come across either very large or very small...
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SIGNIFICANT FIGURES & SCIENTIFIC NOTATION
Sig Figs
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Scientific NotationIn science, we often come across either very large or very small numbers, so we use Scientific Notation as a way to simplify them.
Some numbers hard to work with:
Mass of one atom
= 0.000000000000000000000000000000091 kg
# atoms in 2 grams of hydrogen
= 1200000000000000000000000 atoms
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Scientific NotationEasier:
Mass of one electron = 9.1 x 10-32
# atoms in 2 g hydrogen = 1.2 x 1024
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In Scientific Notation, a number is written as the product of two numbers:
A coefficient, and 10 raised to a power (exponent).
The coefficient is always greater than or equal to 1, and less than 10
M x 10n
M = Coefficient between 1 and 10
10 is the base
n is the exponent
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Scientific Notation Worksheet
Numbers > 1 have a positive exponent
5.2 x 103
Numbers < 1 have a negative exponent
9.65 x 10-4
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The Importance of MeasurementEx: 2011. converted to scientific notation:
In this case: In order for the coefficient to be between 1 and 10, the decimal
has to move 3 places to the left. The decimal moved 3 times, so the value of the exponent is 3 The number (2011) is bigger than 1, so the exponent will be
positive.(103 = 1000., so this reads 2.011 x 1000 which = 2011.)
Ex: 0.036 converted to scientific notation:In this case: In order for the coefficient to be between 1 and 10, the decimal
has to move 2 places to the right. The decimal moved 2 times, so the value of the exponent is 2 The number (0.036) is less than 1, so the exponent will be
negative.(10-2 = 0.01, so this reads 3.6 x 0.01 which = 0.036)
2.011x 10 3+
3.6 x 10 -2
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The Importance of Measurement
1.420 x 10-92 x 106
Convert the following numbers from standard to scientific notation
2 000 000. 0.000 000 001 420
Convert the following numbers from scientific to standard notation
7.29 x 1015
7 290 000 000 000 000.
9.25 x 10-11
0.000 000 000 092 5
Practice
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Significant Figures
We keep track of measurement accuracy through significant digits(Sig Digs) also called significant figures (Sig. Fig)
A measurement is considered to be more accurate if it has more significant digitsSignificant Figures = all known
digits plus one estimated digit
Significant Figures = all known digits
plus one estimated digit
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Significant Figures RULES
1) No zeros? All significant. 377
2) All sandwich zeros significant. 307
3) Leading zeros are not significant. 0.00312
4) If digits are left of a decimal then zeros right of a decimal are significant
3.00
5) Scientific notation indicates significant figures when numbers end in zero
300 = 3 x 102 or 3.00 x 102
When you have to guess, zeros don’t count
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Uncertainty in Measurements
Practice:Count the number of significant digits in each measurement.
0.05730 meters 8.750 x 10-2 centimeters
8765 seconds 200. yards
0.00073 milliliters 200 yards 200.0 yards
40.070 grams 101010 milliseconds
44
4
4
55
3
2 1
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Uncertainty in Measurements
Accuracy is a measure of how close the measurement is to the actual, or “true value” of what was measured.
Actual blood glucose level = 94.899
mg/dL
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Uncertainty in Measurements
Precision is a measure of how close your measurements are to each other.- measurements do not have to be accurate to be precise- measurements can be both precise and accurate, or neither.