Units, Measurement, Significant Figures

1
Units, Measurement, Significant Figures
Conversions

• Physics

2
SI Units

• The SI Units we will be concerned with mostly
  are
• Quantity Unit
• Length/Distance
• Time
• Mass
• Temperature

• meter m
• second s
• kilogram kg
• Kelvin K

3
SI Units

• All of our other units will be based on meters,
  kilograms, seconds, and Kelvins.
• This is referred to as the mks unit system
• Other systems cgs ft/lb/s

4
Making Measurements

• All measurements must contain both
• A number
• A unit
• Measured values are reported such that only the
  last digit is uncertain.
• ALL digits of a measurement, including the last
  one, are called significant figures.

Aka Sig figs
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Measuring Length

• Length measurements are made in units of meters.

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Length Measurements
10
11
12
13
14
?
What is the measurement?
A) 12.92 m B) 12 m C) 12.9 m
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Length Measurements
10
11
12
13
14
?
What is the measurement?
A) 10.3 m B) 10.28 m C) 10 m
8
Length Measurements
10
11
12
13
14
?
What is the measurement?
A) 11.5 m B) 11.55 m C) 11 m
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Sig Fig Rules

• All nonzero digits are significant.
• Ex 2.54 has ____ sig figs
• Ex 167.965 has ____ sig figs
• Zero Rules
• A zero is significant when it appears between two
  nonzero digits
• Ex 2.04 has ____ sig figs
• Ex 10.065 has ____ sig figs

3
6
3
5
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Sig Fig Rules

• Zero Rules cont.
• A zero is significant when it appears at the end
  of a number AND to the right of the decimal
• Ex 4.900 has ____ sig figs
• Ex 17.0 has ____ sig figs

4
3
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Sig Fig Rules

• Zero Rules cont.
• A zero is NEVER significant when it appears in
  front of a number
• Ex 0.007865 has ____ sig figs
• Ex 0.09 has ____ sig fig

4
1
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Sig Fig Rules

• Zero Rules cont.
• A zero is SOMETIMES significant when it appears
  at the end of a number AND to the left of the
  decimal
• For this course, assume these zeros ARE NOT
  significant unless you read precisely or
  exactly in front of the number
• Ex 20 has ____ sig fig
• Ex 3400 has ____ sig figs

1
2
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Sig Fig Rules

• A good rule-of-thumb for the zeros in sig figs is
  this
• Convert the number to scientific notation and if
  the zeros drop out then they are not significant
• Ex 0.007865 7.865 x 10-3
• So it has 4 sig figs
• Ex 3400 3.4 x 102
• So it has 2 sig figs

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Try it!

• How many sig figs are in each of the following?
• 0.000743

A) 3 B) 6 C) 7
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Try it!

• How many sig figs are in each of the following?
• 0.000743
• 10.47

A) 2 B) 3 C) 4
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Try it!

• How many sig figs are in each of the following?
• 0.000743
• 10.47
• 219,976.900

A) 5 B) 9 C) 11
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Try it!

• How many sig figs are in each of the following?
• 0.000743
• 10.47
• 219,976.900
• 4.00000009

A) 2 B) 8 C) 9
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Try it!

• How many sig figs are in each of the following?
• 0.000743
• 10.47
• 219,976.900
• 4.00000009
• 0.0072

A) 2 B) 4 C) 5
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Accuracy Precision

• Two types of numbers in scientific work
• Exact numbers
• Inexact numbers
• Measurements are inexact due to equipment and
  human error.
• Precision accuracy are used to describe the
  uncertainty of measured values.

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Accuracy Precision

• Precision refers to how reproducible individual
  measurements are
• Accuracy refers to how closely individual
  measurements agree with the true or accepted
  value

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Accuracy Precision
Accurate but not precise
Precise but not accurate
22
Accuracy Precision
Neither accurate nor precise
Both accurate and precise
GOOD
BAD
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Unit Conversions

• Notes on board

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Try It!

• 183 cm equals how many meters?
• First, choose a conversion factor
• A) B) C)
• Then do the calculation
• A) 1.83 m B) 18.3 m C) 18300 m

1 m 100 cm
10 mm 1 cm
1,000 m 1 km
25
Try It!

• 8,700 milligrams is how many grams?
• First, choose a conversion factor
• A) B) C)
• Then do the calculation
• A) 0.87g B) 87.0 g C) 8.7 g

1000 mg 1 g
1000 kg 1 g
1 g 1000 mg
26
Try It!

• 4.3 Astronomical Units (A.U.) is equal to how
  many kilometers?
• First, choose a conversion factor
• A) B) C)
• Then do the calculation
• A) 6.4 km B) 6.432 x 108 km C) 6.4 x 108
  km

1 A.U. 149,597,870.7 km
149,597,870.7 km 1 A.U.
149,597.8707 m 1 A.U.