Download Section 2.8 Mathematical Operations in Scientific Notation

Section 2.8
Mathematical Operations in Scientific Notation
Student Learning Focus
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Be able to carry out basic mathematical
operations using numbers expressed in scientific
notation, without changing them to decimal
notation.
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Section 2.8
Mathematical Operations in Scientific Notation
Multiplication and Division in Scientific Notation
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Multiplying and Dividing in scientific notation is
pretty straightforward.
Fewest number of significant figures in the
coefficient.
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Section 2.8
Mathematical Operations in Scientific Notation
Multiplication and Division in Scientific Notation
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(2.05 x 10–3) x (1.19 x 10–7)
Calculator gives 2.4395 x 10–10
But this answer has 5 sig figs in the coefficient
Your calculator does not know about sig figs
The actual answer is 2.44 x 10–10
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Section 2.7
Expressing Numbers in Scientific Notation
Learning Check
Solve the following and express the answer in scientific
notation to the correct number of significant figures.
1. (2.340 x 10–3) x (2.60 x 106)
1. (8.77 x 10–6) x (7.00 x 10–2)
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Section 2.7
Expressing Numbers in Scientific Notation
Solution
Solve the following and express the answer in scientific
notation to the correct number of significant figures.
1. (2.340 x 10–3) x (2.60 x 106)
6084 = 6.08x103
2. (8.77 x 10–6) x (7.00 x 10–2)
0.0000006.14 = 6.14x10–7
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Section 2.8
Mathematical Operations in Scientific Notation
Addition and Subtraction in Scientific Notation
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Addition and Subtraction in Scientific Notation is a
little trickier.
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Remember the rule for significant figures for
addition and subtraction is that the least precise
number sets the limit on the sig figs
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When the exponents are different it is hard to tell
which number is the least precise.
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Section 2.8
Mathematical Operations in Scientific Notation
Addition and Subtraction in Scientific Notation
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1.25 x 10–3 + 6.33 x 10–5
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There are two ways to deal with this
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1. Equalize the exponents
2. Determine the uncertainty for each number and
use the most uncertain (least precise)
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Section 2.8
Mathematical Operations in Scientific Notation
Addition and Subtraction in Scientific Notation
•
1.25 x 10–3 + 6.33 x 10–5
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Equalize the exponents (always use the larger
exponent)
1.25 x 10–3
0.0633 x 10–3
When the coefficients are added the lease precise
value is 1.25 so the answer can only be precise to
the 100ths place
1.25 + 0.0633 = 1.3133 = 1.31 x 10–3
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Section 2.8
Mathematical Operations in Scientific Notation
Addition and Subtraction in Scientific Notation
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1.25 x 10–3 + 6.33 x 10–5
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Determine the uncertainty for each number and use
the number with the larger uncertainty
1.25 x 10–3
10–2 x 10–3 = 10–5 larger uncertainty
6.33 x 10–5
10–2 x 10–5 = 10–7
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The answer must have the same uncertainty –5
0.0013133
= 1.31 x 10–3
10–2 x 10–3 = 10–5
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Section 2.8
Mathematical Operations in Scientific Notation
Learning Check
Solve the following and express the answer in scientific
notation to the correct number of significant figures.
1. (7.431 x 108) + (4.00 x 106)
1. (7.431 x 10–8) – (4.00 x 10–3)
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Section 2.8
Mathematical Operations in Scientific Notation
Solution
Solve the following and express the answer in scientific
notation to the correct number of significant figures.
(7.431 x 108) + (4.00 x 106)
Equalize the exponents
7.431x 108 + 0.0400 x 108
7.4710x106
7.471x108
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Section 2.8
Mathematical Operations in Scientific Notation
Solution
Solve the following and express the answer in scientific
notation to the correct number of significant figures.
(7.431 x 108) + (4.00 x 106)
Determine the uncertainty for each number and use the
larger uncertainty
7.431 x 108
10–3 x 108 = 105
larger uncertainty
4.00 x 106
10–2 x 106 = 104
The answer must have the same uncertainty 104
7.471 x 108
10–3 x 108 = 105
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Section 2.8
Mathematical Operations in Scientific Notation
Solution
Solve the following and express the answer in scientific
notation to the correct number of significant figures
(7.431 x 10–8) – (4.00 x 10–3)
Calculator answer 3.999992569 x 10 – 3
Equalize the exponents
0.00007431 x 10–3 – 4.00 x 10–3
– 4.00 x 10–3
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Section 2.8
Mathematical Operations in Scientific Notation
Solution
Solve the following and express the answer in scientific
notation to the correct number of significant figures.
(7.431 x 10–8) – (4.00 x 10–3)
Determine the uncertainty for each number and use the
larger uncertainty
7.431 x 10–8
10–3 x 10–8 = 10–11
4.00 x 10–3
10–2 x 10–3 = 10–5 larger uncertainty
Calculator answer 3.999992569 x 10 – 3
The answer must have the same uncertainty – 5
– 4.00 x 10–3
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