Measuring Things in the Real World

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Measuring Things in the Real World

• Can you tell me how many students are in this
  room?
• How many molecules of H20 (water) in this
  container?

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Large Numbers

• Distance of Earth to the nearest star, not
  counting the sun is about 39,700,000,000,000 km
  or 4.3 light years or 24,674,000,000,000 mi.
• The diameter of a bacteria is 0.000001 meters (1
  micron or micrometer) or
• The number of water molecules in 18 grams of
  water is about 602,300,000,000,000,000,000,000

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• Can you tell me using a calculator or without
  what
• 280,000,000,0004,100,000,000,000 ?
• How about
• 241,000,000,000 ? 0.00000000135 ?

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Scientific or Exponential Notation

• We take large numbers and write them using powers
  of ten.
• For Example
• Distance of Earth to the nearest star, not
• counting the sun is about
• 39,700,000,000,000 km3.971013 km
• or 4.3 light years or
• 24,674,000,000,000 mi2.4674 1013mi.

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• The diameter of a bacteria is 0.000001
  meters110-6m (1 micron or micrometer) or
• The number of water molecules in 18 grams of
  water is about 602,300,000,000,000,000,000,000
• 6.023 1023 molecules (Avogardos number)

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• Can you tell me using a calculator or without
  what
• 280,000,000,0004,100,000,000,000
• 2.8 1011 4.1 1013 4.128 1013
• How about
• 241,000,000,000 ? 0.00000000135
• 2.41 1011 ? 1.35 10-91.7852 1020

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How Big is it?

• US national debt is over 6 trillion dollars.
• What does that mean? How much is it?
• Well lets consider how many years it would take
  if paid the debt 1 dollar per second.

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Paying the National Debt

• There are 60 seconds in a minute and 60 minutes
  in an hour and 24 hours in a day and 365 days in
  a year. That is

• 60 60 24 365 315.36 60 105 seconds in a
  year.

It will take more than 190 thousand years to pay
the debt at this rate.
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Logarithmic Scales

• Huge data is plotted on a logarithmic scales
  which uses powers of tens for scale of lengths.
• In astronomy they use light years (distance
  covered by a light ray in one year) to talk about
  large distances.
• 1 light year9.4606 1015 meters?mi (use 1000
  meters0.621504 mi)

• 1 light year58.8 1012 miles

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Real World Measurements Dealing with units

• If I told you that in India a professor makes
  50,000 rupees/year in the University of Pune (in
  India), would you know how much money that really
  is?
• Speed of light is 2.9979 ?108 meter/sec, do you
  have a sense of how fast it is?

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• One dollar50 rupees and so 50,000 rupees1000
  rupees
• 1 mile1,609 meters or 1.609 kilometers and so
  the speed of light is 2.9979 ?108 meter/sec?
  mi/sec

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• Area of a room is 50 sq feet.
• The turkey will cost you 2 dollars/pound.
• Suppose I traveled 2 mi and then 3 km, can I say
  I traveled a total of 5 mi or 5 km?

We can say I traveled for 3.8645 mi or 6.218 km.
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Conversion of Units

• Converting from miles to kilometers

Multiply by 0.6215
Miles
Kilometers
Multiply by 1.609
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• Whenever you deal with unit conversion treat the
  units as variables and you will be able to
  convert from one unit to another without much
  trouble.

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• Example Convert 25 square miles per
• hour to square kilometers per sec.

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• Example 2 Suppose it cost 60
• Rupees/liter for petrol in India. How
• many dollars per gallon is the price of
• petrol in India?
• Note that 1 liter0.26425 gallons and
• 50 Rupees1 dollar.

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Solution

• In India it will cost 4 dollars and 54 cents
• per gallon to buy gas or petrol.

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• THE END