A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0009658 in scientific notation is 9.658 x 10^-4

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To subtract these radicals together their radicands must be the same:

7\( \sqrt{32} \) - 6\( \sqrt{2} \)
7\( \sqrt{16 \times 2} \) - 6\( \sqrt{2} \)
7\( \sqrt{4^2 \times 2} \) - 6\( \sqrt{2} \)
(7)(4)\( \sqrt{2} \) - 6\( \sqrt{2} \)
28\( \sqrt{2} \) - 6\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

36,000 fans x \( \frac{2}{3} \) = \( \frac{72000}{3} \) = 24,000 fans.