This web page provides a review of the mathematical concepts you will apply in this
course.

Fractions are a part of every-day life and they are also used in science. A
fraction with the same numerator (number on top) as another but with a smaller
denominator (number on bottom) is a *larger* number. For example 1/2 is
*bigger* than 1/3 which is bigger than 1/4, etc. That is because if you
divide 1 by 2, you get 0.5 but 1 divided by 3 is only 0.333 and 1 divided by
4 is only 0.25. The fraction 3/5 (=0.6) is bigger than 3/6 (=0.5) which is
bigger than 3/7 (=0.4286).
Fractions are sometimes expressed as a **percent**. To express a fraction as
a percentage, find the decimal form and multiply by 100. The percent symbol
``%'' simply means ``divide by 100.'' For example 1/2 = 0.5 =
0.5× 100% = 50%; 3/5 = 0.6 = 0.6× 100% = 60%. Some examples
on converting percentages to fractions or decimals: 5.8% = 5.8/100 = 0.058;
0.02% = 0.02/100 = 0.0002; the Sun is 90% hydrogen means that 90 out of every
100 atoms in the Sun is hydrogen.

Several homework questions ask you to find some quantity and find out how many
``times'' smaller or larger it is than something else, e.g., star A is
____times larger than star B. This means star A
= a × star B, and you must find the number
a. Another
example: A gallon is equivalent to 4 quarts. This means that 1 gallon is 4
**times** *bigger* than 1 quart since 1 gallon = 4 × 1 quart, or
(1 gallon)/(1 quart) = 4/1. This also means that 1 quart is 4 **times**
*smaller* than 1 gallon since 1 quart = 1/4 × (1 gallon), or
(1 quart)/(1 gallon) = 1/4. Notice when ``times bigger'' is used and when
``times smaller'' is used.
The use of the phrase ``factor of'' is very similar to the use of ``times''.
For example, 1 quart is a **factor of** 4 *smaller* than 1 gallon, or
1 gallon is a **factor of** 4 *bigger* than 1 quart.

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last updated: 08 August 2001

##### Is this page a copy of Strobel's
Astronomy Notes?

Author of original content:
Nick Strobel