9/8/2016
Scientific notation – a shorthand
way of writing very large or very
small numbers
• Numbers are always written as a product of a
factor and a power of 10.
Scientific Notation
• Neptune is 2,800,000,000 miles from the sun.
2.8 x 109 miles
I can convert between standard notation and scientific notation.
I can use scientific notation to compare the relative sizes of
numbers.
Scientific Notation
• The factor must be between 0 and 10 (the ones
digit can only be 1-9).
• All nonzero digits and any zeroes between
nonzero digits are important.
• The exponent must be an integer (no decimals
or fractions).
• Large (whole) numbers have positive exponents.
• Small (decimal) numbers have negative exponents.
Writing in Scientific Notation
28,046,000
0.00408
Which numbers are written in
scientific notation?
A.
B.
C.
D.
E.
4.96 × 10−3
8.216 × 104.1
24 × 109
6.5041 × 1012
3.42 × 115
F. 3.84 × 83
G. 1.563 × 10−6
H. 0.04 × 10−7
Writing in Scientific Notation
• Put an X after the 1st nonzero digit.
• Count how many places back to the decimal (this
is your exponent).
• Count back to the left → negative
• Count back to the right → positive
• Rewrite factor without placeholder zeroes.
32,000
0.0000129
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9/8/2016
Write in scientific notation.
a) 3,900,400
b) 0.0023
c) 49,000,000,000,000
d) 0.000005608
e) 0.009
Describe and correct the error in
writing the number in scientific
notation.
Describe and correct the error in
writing the number in scientific
notation.
Interpreting Calculator
Answers
• The number in front is the
factor.
• The number after E is the
exponent.
• Replace E with 10^ when
writing your answer.
Writing in standard notation
Writing in standard notation
3.22 × 10−4
7.9 × 105
• Negative exponents give
decimal answers.
• Move decimal 4 places
LEFT to get decimal
answer.
• Positive exponents give
whole number answers.
• Move decimal 5 places
RIGHT to get whole
number answer.
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9/8/2016
Writing in Standard Notation
Write each number in scientific
notation AND standard notation.
• The exponent tells you how many places to
move the decimal.
• Positive exponent → move decimal right
• Negative exponent → move decimal left
(Think of a number line!)
• Fill in any holes with zeroes.
6.42 × 10−5
4.917 × 107
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