Mrs. Kristen Kauffman Legacy High School Chemistry I Measurement & Scientific Notation.
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Transcript of Mrs. Kristen Kauffman Legacy High School Chemistry I Measurement & Scientific Notation.
![Page 1: Mrs. Kristen Kauffman Legacy High School Chemistry I Measurement & Scientific Notation.](https://reader036.fdocuments.us/reader036/viewer/2022062306/5a4d1b1a7f8b9ab0599932f5/html5/thumbnails/1.jpg)
Mrs. Kristen KauffmanLegacy High School
Chemistry I
Measurement &
Scientific Notation
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What is Data?• Data is any type of information.• Data–Qualitative = description in words• The solution is blue.
–Quantitative = measurement with numbers• The solution has a volume of 42.7 mL.
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What Is a Measurement?• Quantitative
observation.• Comparison to an
agreed upon standard.• Every measurement
has a number and a unit.– The unit tells you to
what standard you are comparing your object.
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Scientists have measured the average global temperature rise over the past century to be 0.6 °C
• °C tells you that the temperature is being compared to the Celsius temperature scale.
• 0.6 tells you that:1. The average temperature rise is
0.6 times the standard unit of 1 degree Celsius.
2. The confidence in the measurement is such that we are certain the measurement is between 0.5 and 0.7 °C.
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Scientific Notation
A way of writing large and small numbers.
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Big and Small Numbers
• We commonly measure objects that are many times larger or smaller than our standard of comparison.
• Writing large numbers of zeros is tricky and confusing.– Not to mention there’s the
8-digit limit of your calculator!
The sun’sdiameter is
1,392,000,000 m.
An atom’s average diameter is0.000 000 000 3 m.
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Scientific Notation
• Each decimal place in our number system represents a different power of 10.
• Scientific notation writes the numbers so they are easily comparable by looking at the power of 10.
The sun’sdiameter is
1.392 x 109 m.
An atom’s average diameter is
3 x 10-10 m.
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Exponents
• When the exponent on 10 is positive, it means the number is that many powers of 10 larger. – Sun’s diameter = 1.392 x 109 m =
1,392,000,000 m.• When the exponent on 10 is negative,
it means the number is that many powers of 10 smaller.– Average atom’s diameter = 3 x 10-10 m =
0.0000000003 m.
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Scientific Notation• To compare numbers written in
scientific notation:– First compare exponents on 10.– If exponents are equal, then compare
decimal numbers
1.23 x 10-8
Decimal part Exponent part
Exponent
1.23 x 105 > 4.56 x 102
4.56 x 10-2 > 7.89 x 10-5
7.89 x 1010 > 1.23 x 1010
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Writing Numbers in Scientific Notation
1. Locate the decimal point.2. Move the decimal point so that there
is only 1 nonzero digit to the left of it.3. Multiply the new number by 10n .– Where n is the number of places you
moved the decimal point.4. If you moved the decimal point to the
left, then n is +; if you moved it to the right, then n is − .– If the original number is 1 or larger, then
n is + .– If the original number is less than 1, then
n is − .
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123401. Locate the decimal point.
12340.2. Move the decimal point so that there is only 1
nonzero digit to the left of it.1.234
3. Multiply the new number by 10n .– Where n is the number of places you moved the
decimal point.1.234 x 104
4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − .
1.234 x 104
Writing a Number in Scientific Notation, Continued
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Writing a Number in Scientific Notation, Continued
0.000123401. Locate the decimal point.
0.000123402. Move the decimal point to obtain a number
between 1 and 10.1.2340
3. Multiply the new number by 10n .– Where n is the number of places you moved the
decimal point.1.2340 x 104
4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − .
1.2340 x 10-4
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Writing a Number in Standard Form1.234 x 10-6
• Since exponent is -6, make the number smaller by moving the decimal point to the left 6 places.–When you run out of digits to move
around, add zeros.– Add a zero in front of the decimal
point for decimal numbers.000 001.2340.000 001 234
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Sci. Notation Example• The U.S. population in 2007 was
estimated to be 301,786,000 people. Express this number in scientific notation.
• 301,786,000 people = 3.01786 x 108 people
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Practice—Write the Following in Scientific Notation
123.4
145000
25.25
1.45
8.0012
0.00234
0.0123
0.000 008706
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Practice—Write the Following in Scientific Notation, Continued
123.4 = 1.234 x 102
145000 = 1.45 x 105
25.25 = 2.525 x 101
1.45 = 1.45 x 100
8.0012 = 8.0012 x 100
0.00234 = 2.34 x 10-3
0.0123 = 1.23 x 10-2
0.000 008706 = 8.706 x 10-6
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Practice—Write the Following in Standard Form
2.1 x 103
9.66 x 10-4
6.04 x 10-2
4.02 x 100
3.3 x 101
1.2 x 100
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Practice—Write the Following in Standard Form, Continued
2.1 x 103 = 2100
9.66 x 10-4 = 0.000966
6.04 x 10-2 = 0.0604
4.02 x 100 = 4.02
3.3 x 101 = 33
1.2 x 100 = 1.2
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Multiplying and Dividing in Scientific Notation
• Multiplying– Multiply the two decimal parts of each number
and ADD the exponents• (3.32x105) * (2.56x107) = 8.50x1012
• Dividing– Divide the two decimal parts of each number
and SUBTRACT the exponents• (8.56x1017) / (3.61x104) = 2.37x1013
• You may need to convert the final answer into proper scientific notation by moving the decimal and changing the exponent– (5.87x103) * (6.53x105) = 38.33x108 =
3.833x109
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Inputting Scientific Notation into a Calculator
• Input the decimal part of the number.– If negative press
+/- key.• (–) on some.
• Press EXP.– EE on some.
• Input exponent on 10.– Press +/- key to
change exponent to negative.
-1.23 x 10-3
-1.23 -03
Press +/-
Input 1.23 1.23
Press EXP -1.23 00
Input 3 -1.23 03
-1.23 Press +/-