astronomical numbers snc1d. powers of ten numbers in astronomy are often much larger than we are...
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Astronomical Numbers
SNC1D
Powers of Ten
Numbers in astronomy are often much larger than we are used to dealing with in daily life.
We often express them in terms of powers of ten.
Example: 1 000 000 000 = 109
Scientific Notation
Scientific notation may be used to write numbers in terms of powers of ten.
Example:m111050.1
This coefficient must have an absolute value between 1 and 10. All significant digits must be shown.
Large Numbers
To write a large number in scientific notation, count how many places to the left you have to move the decimal until it is after the first non-zero.
This is your power of ten.
Small Numbers
For small numbers, you count places to the right. This is your negative power of ten.
Practice
Write each of the following in scientific notation:
• 43800 =• 0.050 =• 7100000000 =• 0.00088 =• 10.1 =
Practice
Write each of the following in scientific notation:
• 43800 = 4.38 x 104
• 0.050 =• 7100000000 =• 0.00088 =• 10.1 =
Practice
Write each of the following in scientific notation:
• 43800 = 4.38 x 104
• 0.050 = 5.0 x 10-2
• 7100000000 =• 0.00088 =• 10.1 =
Practice
Write each of the following in scientific notation:
• 43800 = 4.38 x 104
• 0.050 = 5.0 x 10-2
• 7100000000 = 7.1 x 109
• 0.00088 =• 10.1 =
Practice
Write each of the following in scientific notation:
• 43800 = 4.38 x 104
• 0.050 = 5.0 x 10-2
• 7100000000 = 7.1 x 109
• 0.00088 = 8.8 x 10-4
• 10.1 =
Practice
Write each of the following in scientific notation:
• 43800 = 4.38 x 104
• 0.050 = 5.0 x 10-2
• 7100000000 = 7.1 x 109
• 0.00088 = 8.8 x 10-4
• 10.1 = 1.01 x 101
You can go from scientific to standard notation by simply moving the decimal back. . . .
More Practice
Write each of the following in standard notation:
• 5.1 x 103 =• 8.2 x 10-3 =• 3.00 x 106 =• 4.0 x 10-5 =• 5.75 x 10-1 =
More Practice
Write each of the following in standard notation:
• 5.1 x 103 = 5100• 8.2 x 10-3 =• 3.00 x 106 =• 4.0 x 10-5 =• 5.75 x 10-1 =
More Practice
Write each of the following in standard notation:
• 5.1 x 103 = 5100• 8.2 x 10-3 = 0.0082• 3.00 x 106 =• 4.0 x 10-5 =• 5.75 x 10-1 =
More Practice
Write each of the following in standard notation:
• 5.1 x 103 = 5100• 8.2 x 10-3 = 0.0082• 3.00 x 106 = 3000000• 4.0 x 10-5 =• 5.75 x 10-1 =
More Practice
Write each of the following in standard notation:
• 5.1 x 103 = 5100• 8.2 x 10-3 = 0.0082• 3.00 x 106 = 3000000• 4.0 x 10-5 = 0.000040• 5.75 x 10-1 =
More Practice
Write each of the following in standard notation:
• 5.1 x 103 = 5100• 8.2 x 10-3 = 0.0082• 3.00 x 106 = 3000000• 4.0 x 10-5 = 0.000040• 5.75 x 10-1 = 0.575
But you don’t have to change to standard notation to enter the number into your calculator. . . .
Using Your Calculator
Practice
Try:
(5.0 x 103)(6.2 x 1011)
Practice
Try:
(5.0 x 103)(6.2 x 1011)
Answer:
3.1 x 1015
More Practice
Try:6.4 x 1015
4.0 x 10-4
More Practice
Try:6.4 x 1015
4.0 x 10-4
Answer:1.6 x 1019
Other Units
Sometimes astronomical numbers are given with reference to a standard.
Example: 1 Solar Mass = 1.99 x 1030 kgThe star Rigel has a mass
of 3.58 x 1031 kg or 18 Solar Masses.
Astronomical Units
Distances in the solar system are often even in Astronomical Units (AU).
1 AU is the distance from the Earth to the Sun.= 1.50 x 1011 m
Astronomical Units
What is the distance from Mars to the Sun in m?
Astronomical Units
What is the distance from Mars to the Sun in m?
1.52(1.50 x 1011 m) = 2.28 x 1011 m
Light Years
Distances outside the solar system are often given in light years.
1 light year is the distance light travels in a year
= 9.46 x 1015 m
Addendum
To convert km to m, add 3 to the exponent.(Remember that 103 = 1000.)
1.50 x 108 km = 1.50 x 1011 m
(To convert m to km, subtract 3 from the exponent.)