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3.1
Scientific
Using and
Notation
Expressing
& Significant
Measurements
Figures Notes
>
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3.1 Using and Expressing Measurements >
Scientific Notation
• A *measurement is a quantity that
has both a number and a unit.
In scientific notation, a given
number is written as the product of
two numbers = a coefficient x 10n
*n = exponent
Example:
602,000,000,000,000,000,000,000
 6.02 x 1023
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3.1 Using and Expressing Measurements > Scientific Notation
How to Write in Scientific Notation
If the coefficient > 10
Decimal moves to the left
# spaces = n  +
If the coefficient < 1
Decimal moves to the right
# spaces = n  -
6,300,000. = 6.3 x 106
0.000 008 = 8 x 10-6
94,700. = 9.47 x 104
0.00736 = 7.36 x 10-3
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3.1 Using and Expressing Measurements >
Practice Problems #1:
Write the following in scientific notation.
①
②
③
④
⑤
⑥
3,400 =
101,000 =
45.01 =
0.000023 =
0.010 =
1,000,000 =
***DO PRACTICE PROBLEMS ON THE BOARD***
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3.1 Using and Expressing Measurements >
***REMEMBER***
Move the decimal point until you
have 1 WHOLE NUMBER to
the LEFT OF DECIMAL POINT!
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3.1 Using and Expressing Measurements > Scientific Notation
Multiplication and Division
To multiply: multiply the coefficients and add the n.
(3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106
(2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4
To divide: divide the coefficients and subtract the
n(numerator – denominator).
3.0 x 105
=
2
6.0 x 10
6
3.0
6.0
( )
x 105–2 = 0.5 x 103
= 5.0 x 102
3.1 Using and Expressing Measurements >
Practice Problems #2:
Solve the following problems and write your answers in
scientific notation.
①
②
③
④
⑤
(8.0 x 10–2) x (7.0 x 10–5) =
(6.6 x 106)  (2.2 x 102) =
(5.0 x 106)  (2.0 x 104) =
(3.0 x 10–3) x (2.5 x 10–4) =
(8.8 x 10–2) x (2.5 x 103) =
***DO PRACTICE PROBLEMS ON THE BOARD***
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3.1 Using and Expressing Measurements > Significant Figures
*Significant Figures
• The significant figures in a measurement
include all of the digits that are known, plus
a last digit that is estimated.
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3.1 Using and Expressing Measurements > Significant Figures
Rules of Significant Figures
1. Every nonzero digit is significant.
24.7 m
0.743 m
714 m
2. Zeros appearing between nonzero digits are
significant.
7003 m
40.79 m
1.503 m
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3.1 Using and Expressing Measurements > Significant Figures
Determining Significant Figures in Measurements
3. All zeros on the left are not significant. To
eliminate, write the number in scientific notation.
0.0071 m
= 7.1 x 10-3 m
0.42 m
= 4.2 x 10-1 m
0.000 099 m = 9.9 x 10-5 m
4. To be significant, Zeros must be after a number
and after the decimal point.
43.00 m
1.010 m
9.000 m
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3.1 Using and Expressing Measurements > Significant Figures
Determining Significant Figures in Measurements
5. Zeros in front of the decimal point are not
significant.
300 m
7000 m
27,210 m
If zeros were exact measurements, then they’re
significant. Write the value in scientific
notation.
300 m =
3.00 x 102 m
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3.1 Using and Expressing Measurements >
Practice Problems #3:
Determine the number of sig figs.
①
②
③
④
⑤
⑥
6.571 g 
2500 m 
0.157 kg 
0.0700000 g 
28.0 ml 
30.07 g 
***DO PRACTICE PROBLEMS ON THE BOARD***
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3.1 Using and Expressing Measurements > Significant Figures
Significant Figures in Calculations
Rounding
• 1. decide how many significant figures
• 2. round to that many digits
• Note:
• If the next number is <5, digit stays
the same.
• If the next number is ≥5, round up.
For Example:
a. 314.721 m (four) 
b. 0.001 775 m (two) 
c. 8792 m (two) 
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314.7 m
0.0018
8800
3.147 x 102
m 1.8 x 10-3 m
8.8 x 103 m
3.1 Using and Expressing Measurements > Significant Figures
Significant Figures in Calculations
Multiplication and Division
• Round the answer to the same number of
significant figures as the measurement
with the least number of significant
figures.
7.55 m x 0.34 m = 2.567 m2
= 2.6 m2
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3.1 Using and Expressing Measurements >
Practice Problems #4:
Solve the following problems. Write the answers in the
correct number of sig figs and in scientific notation.
①
②
③
④
2.10 m x 0.70 m
0.365 m2  0.0200 m
2.4526 m2  8.4 m
8.3 m x 2.22 m
***DO PRACTICE PROBLEMS ON THE BOARD***
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