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Scientific Notation

Metric System and Astronomical Constants

Metric System

The Metric System was developed in the 18th Century for scientific studies and calculations. In the US, most people use the English System which has inches, feet, miles, pounds and tons to describe Length and Mass (weight). These units are hard to calculate because of how the units relate to each other. For instance, 12 inches are in a foot, 5,280 feet in a mile, 16 ounces in a pound, 2,000 pounds in a ton and so on. To find the area of a room, you might have 8 feet 10 inches on one wall and 10 feet 6 inches on the other. You would have to convert the numbers to inches and divide by 144 (12 inches x 12 inches = 1 square foot) to get the square feet of area. This can be a lot of work when the numbers are large like 93,000,000 (ninty-three million) miles, the average distance from the Earth to the Sun. See the conversion chart below to compare units.

In the Metric System Length is described in meters, Mass is listed in kilograms and Time is related in seconds. Each unit can increased by factors of ten or decreased by the factor of ten making the calculations easier than in the English Sytem. Note that prefixes like kilo (thousand), mega (million), centi (hundredth), and milli (thousandth) can be used to modify the units. For example, a kilometer is 1,000 meters and a centimeter is 0.01 meter. An object could be describes as moving 1 km/sec or weighing 3 grams (3 thousandths of a kilogram).

Temperature is given in degrees Celsius or Kelvin. The Celsius scale started as the Centigrade scale because Swedish astronomer Anders Celsius invented a thermometer that had 100 degrees between the freezing point of water or 0 degrees and boiling at 100 degrees. You may have noticed weather temperatures listed for Canada in Celsius. William Thomson, Lord Kelvin of Scotland developed the scale that bears his name that sets Absolute Zero at 0 Kelvin, freezing at 273 K and boiling at 373 K. Add 273 to the Celsius reading to convert to Kelvin or subtract 273 to convert to Celsius.

Meters
Inches
Feet
Yards
Miles
Nautical Miles
Enter a number, then click "Calculate":

Scientific Notation

Using factors of 10 to write large or small numbers is not only easier to understand but simple to do. For example the number 100,000 can be written as 1 x 105 or even 100 x 103. An easy way is to count the number of zeros in the number. This makes writing the distance from the sun to Alpha Centauri, the nearest star, 4.3 x 1013 km easier than 43,000,000,000,000 (Forty-three trillion) km. Note that you have 12 zeros plus one more power of ten because the decimal point is between the 4 and the 3.

Numbers smaller than one use a minus sign in the notation to indidate the place value. One one hundredth or .01 is the same as 1 x 10-2. See the table below for other examples.

1 x 1014 = 100,000,000,000,000
1 x 105 = 100,000
1 x 104 = 10,000
1 x 103 = 1,000
1 x 102 = 100
1 x 101 = 10
1 x 100 = 1
1 x 10-1 = 0.1
1 x 10-2 = 0.01
1 x 10-3 = 0.001
1 x 10-4 = 0.0001
1 x 10-5 = 0.00001

Common Astronomical Constants

These values are uses to describe various astronomical properties.

Common Astronomical Constants
Constant Value   Constant Value
Parsec 3.26 Light Years Parsec 206,265 AU
Light Year 9.461 x 1015 meters Velocity of Light 2.998 x 108 m/sec
Astronomical Unit (AU) 1.496 x 1011 meters Absolute Zero 0° Kelvin
Water Freezes 273° Kelvin Water Boils 373° Kelvin

Quick Check

To check your understanding, fill in the blanks.
Have your teacher or a parent check your work.

  1. The Earth has a mass of 5.976 x 1024 kg.
    Write this as a whole number   _______________________________.
  2. The lowest temperature of Mars is -140° C.
    Write this in Kelvin  __________________________.
  3. Write 1200 meters in the units below:
    Kilometers __________ Centimeters __________
    Millimeters __________ Scientific Notation __________X10(   ) meters
  4. Mercury's average distance from the sun is 57,910,000 km.
    Write it in Scientific Notation: __________.

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