Significant Digits

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Significant Digits   all the digits that occupy
places for which actual measurements are made,
plus ONE estimated digit
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2
1
1
2
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When we are measuring quantities, the instrument
we use will determine the precision of the
quantity. For example, if we are using an
electronic balance that goes to 3 decimal places,
our answer should go to 3 decimal places.
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Rules for counting sig figs

• Digits other than zero are always significant.
• 96
• 61.4
• Zeroes between 2 other sig figs are always
  significant.
• 5.029
• 306

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3
4
3
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Rules for Counting Sig Figs, cont.

• If in doubt, use the Atlantic/Pacific Rule
• If the decimal is present, start counting from
  the left (Pacific side) until you reach the first
  non-zero number. That number and everything
  after is significant.
• If the decimal is absent, start counting from the
  right (Atlantic side) until you reach the first
  non-zero number. That number and everything
  after it is significant.
• 4.7200
• 0.082
• 7000
• 8030

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2
1
3
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Rules for calculating with sig figs

• In addition and subtraction, the answer should be
  rounded off so that it has the same number of
  decimal places as the quantity having the least
  number of decimal places.
• In multiplication and division, the answer should
  have the same number of significant digits as the
  given data value with the least number of
  significant digits.
• 4.60 ? 45
• 1.956 ? 3.3
• 1.1 225
• 2.65 1.4

207
210
0.5927
0.59
226.1
226
1.25
1.3
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Scientific Notation

• A method to write very large or very small
  numbers
• Coefficient any number from 1-9
• Exponent shows the number of times 10s are
  multiplied together ( 102
  )

10 ? 10
100
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Changing Standard Numbers to Scientific Notation

• Numbers greater than 10
• Move decimal until only ONE number is to the left
  of the decimal.
• The exponent is the number of places the decimal
  has moved and it is POSITIVE.
• Ex. 125
• 15,000,000,000

1.25 ? 102
1.5 ? 1010
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Changing Standard Numbers to Scientific Notation,
cont.

• Numbers less than 1
• Move decimal until only one number is to the left
  of the decimal.
• The exponent is the number of places the decimal
  has moved and it is NEGATIVE.
• Ex. 0.000189
• 0.5476

1.89 ? 10-4
5.476 ? 10-1
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Changing Standard Numbers to Scientific Notation,
cont.

• To change a number written in incorrect
  scientific notation
• Move the decimal until only one number is to the
  left of the decimal.
• Correct the exponent. (remember take away, add
  back)
• Ex. 504.2 ? 106
• 0.0089 ? 10-2

5.042 ? 108
8.9 ? 10-5
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Changing Numbers in Scientific Notation to
Standard Notation

• If the exponent is () move the decimal to the
  right the same number of places as the exponent.
• 1.65 ? 101
• 1.65 ? 103
• If the exponent is (-) move the decimal to the
  left the same number of places as the exponent.
• 4.6 ? 10-2
• 1.23 ? 10-3

16.5
1650
0.046
0.00123
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Multiplication and Division with Scientific
Notation

• To multiply numbers in scientific notation
• Multiply the coefficients.
• Add the exponents.
• Convert the answer to correct scientific
  notation.
• Ex (2 ? 109) x (4 ? 103)

8
? 1012
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Multiplication and Division with Scientific
Notation, cont.

• To divide numbers in scientific notation
• Divide the coefficients.
• Subtract the exponents.
• Convert the answer to correct scientific
  notation.
• Ex (8.4 ? 106) ? (2.1 ? 102)

4
? 104
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Addition and Subtraction with Scientific Notation

• Before numbers in scientific notation can be
  added or subtracted, the exponents must be equal.
• Ex. (5.4 ? 103) (6.0 ? 102)

(5.4 ? 103) (0.6 ? 103)
6.0 ? 103
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T w o S y s t e m s

• M e t r i c
• M e t e r
• Gram
• Liter
• Celsius

• E n g l i s h
• yard, mile, feet
• pound, ounce
• quart, gallon
• Fahrenheit

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Metric System
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F a c t o r - L a b e l
M e t h o d

• W h a t i s i t ?

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F a c t o r - L a b e l

• T h e m o s t i m p o r t a n t
  m a t h e m a t i c a l p r
  o c e s s for scientists .
• T r e a t s n u m b e r s a n d
  u n i t s e q u a l l y .
• M u l t i p l y w h a t i s g i v e n
  b y f r a c t i o n s e q u a l t o
  o n e t o c o n v e r t u n i t s .

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F a c t o r - L a b e l
A f r a c t i o n e q u a l t o o n e
W h a t i s g i v e n
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F a c t o r - L a b e l
H o w m a n y b a s k e t b a l l s c a n
b e c a r r i e d b y 8 b u s e s ?
1 bus 12 cars 3 cars 1
truck 1000 basketballs 1 truck
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F a c t o r - L a b e l
H o w m a n y b a s k e t b a l l s c a n
b e c a r r i e d b y 8 b u s e s ?

1 bus 12 cars 3 cars 1 truck 1000
basketballs 1 truck
8 buses
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F a c t o r - L a b e l
H o w m a n y b a s k e t b a l l s c a n
b e c a r r i e d b y 8 b u s e s ?

1 bus 12 cars 3 cars 1 truck 1000
basketballs 1 truck
12 cars
8 buses
1 bus
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F a c t o r - L a b e l
H o w m a n y b a s k e t b a l l s c a n
b e c a r r i e d b y 8 b u s e s ?

12 cars
1 truck
8 buses
3 cars
1 bus
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F a c t o r - L a b e l
H o w m a n y b a s k e t b a l l s c a n
b e c a r r i e d b y 8 b u s e s ?

1000 bballs
12 cars
1 truck
8 buses
1 truck
1 bus
3 cars
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F a c t o r - L a b e l
3 2 0 0 0 b a s k e t b a l l s c a n b e
c a r r i e d b y 8 b u s e s .
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F a c t o r - L a b e l
C o n v e r t 4 4 g r a m s t o k i l o
g r a m s .
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F a c t o r - L a b e l
C o n v e r t 4 4 g r a m s t o k i l o g
r a m s
4 4 g
0 . 0 0 1 k g

0 . 0 4 4 k g
1 g
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F a c t o r - L a b e l
C o n v e r t 8 . 3 c e n t i m e t e r s t
o m i l l i m e t e r s .



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F a c t o r - L a b e l
C o n v e r t 8 . 3 c e n t i m e t e r s t
o m i l l i m e t e r s
8.3 cm
1 m 100 cm
1000 mm 1 m

83 mm
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F a c t o r - L a b e l
M e t h o d