Transcript Scientific Notation

Scientific Notation
Scientific Notation is a convenient way to write
a very small or a very large number.
In science and chemistry, large and small
numbers are frequently encountered
Why?
Scientific Notation
Numbers are written as a product of a number between 1
and 10, times the number 10 raised to power.
General form is: M x 10n
where; 10 > M ≥ 1 and n is any positive or
negative integer
617 is written in scientific notation as:
617 = 6.17 x 100 = 6.17 x (10 x 10) = 6.17 x 102
Scientific Notation
Note: When shifting a decimal to the left the
power of ten moves in a positive direction and
when shifting the decimal to the right, the
power of ten moves in a negative direction.
e.g. 0.006 3 kg becomes 6.3 x 10-3 kg
e.g. 14,700 oz. becomes 1.47 x 104 oz.
Two examples of converting standard notation to
scientific notation are shown below.
Copyright © 2010 Pearson Education, Inc.
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Chapter Two
Expanding into Ordinary Form
Note: When shifting a decimal to the left the power of ten
moves in a positive direction and when shifting the decimal to
the right, the power of ten moves in a negative direction.
A negative power must be shifted left to get back to 100 and a
positive power has to be shifted to the right to get back to
100.
Also, recall, positive powers mean the numbers value is
greater than one and negative powers mean the numbers
value is less than one.
e.g. 4.551 x 10+3 g = 4,551 g
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Expanding into Ordinary Form
Also, recall, positive powers mean the numbers
value is greater than one and negative powers
mean the numbers value is less than one.
e.g. 4.551 x 10+3 g = 4,551 g
e.g. 9.23 x 10-2 km = 0.092 3 km
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Two examples of converting scientific notation back to
standard notation are shown below.
Copyright © 2010 Pearson Education, Inc.
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Chapter Two
Adding and Subtracting with Scientific
Notation
When adding or subtracting in scientific
notation form, the powers of ten MUST be the
SAME.
If the powers of ten are different, temporarily
shift the decimal in order to obtain like powers
of ten.
Adding and Subtracting with Scientific
Notation cont’d
Once like powers of ten are obtained, add or
subtract the digit (or coefficient) terms as called
for in the problem.
The power of ten is retained.
Account for significant figures and return the
result to proper or standard scientific notation
form.
Example Problem
7.9 x 10+2 kg + 9.34 x 10+3 kg =
0.79 x 10+3 kg + 9.34 x 10+3 kg =
(0.79 + 9.34) x 10+3 kg = 10.13 x 10+3 kg
Accounting for sig figs and proper form:
1.013 x 10+4 kg
Example Problem
6.982 x 10-3 hm - 2.881 x 10-4 hm =
6.881 x 10-3 hm - 0.288 1 x 10-3 hm =
(6.881 – 0.288 1) x 10-3 hm = 6.592 9 x 10-3 hm
Accounting for sig figs and proper form:
6.593 x 10-3 hm
Example Problem
2.87 x 102 L + 4.34 x 102 L =
(2.87 + 4.34) x 102 L =
Accounting for sig figs and proper form:
7.21 x 102 L
Note: When adding or subtracting, remember
the units of the quantity MUST be the SAME.
Multiplying in Scientific Notation
When multiplying in scientific notation, the
digit (or coefficient) terms are multiplied and
the powers of ten are SUMMED (added).
Account for significant figures and return the
result to proper or standard scientific
notation form.
Example Problems
4.11 x 103 m x 7.100 x 102 m =
(4.11 x 7.100) x 10(3 + 2) m2 = 29.181 x 105 m2
Accounting for significant figures and proper
form:
= 2.92 x 106 m2
Example Problem
3.233 x 10-3 km x 7.4 x 105 km =
(3.233 x 7.4) x 10(-3 + 5) km2 =
23.924 2 x 10+2 km2
Accounting for Significant figures and proper
form:
2.4 x 10+3 km2
Dividing with Scientific Notation
When dividing numbers in scientific notation
form, the digit or coefficient terms are
divided (dividend by divisor or numerator by
denominator) and the divisor or denominator
power of ten is subtracted FROM the
dividend or numerator power of ten.
Account for significant figures and return to
proper form if necessary.
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Example Problem
Perform the division:
3.54 x 10-2 m2 ÷ 6.88 x 10-3 m =
(3.54 ÷ 6.88) x 10-2-(-3) (m2 ÷ m) =
0.514 534 884 x 10+1 m =
Accounting for Sig figs and proper form.
5.15 x 100 m
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Example Problem
A car travels 4.324 x 103 miles in 6.77 x 101 hours.
What was its average speed?
Equation: s = d / t
= 4.324 x 103 miles ÷ 6.77 x 101 hours =
(4.324 ÷ 6.77) x 103 - 1 (mi ÷ hr) =
0.638 700 148 x 10+2 m =
Accounting for Sig figs and proper form.
6.39 x 10+1 mi/hr
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