Scientific Notation

Example: 152000000 = 1.52^8 (move 8 places to the left)

Exponents

Note: ^ = raised to the power of
Based = the number, Exponent is the power

Example 1: 4*4*4 = 4^3
Example 2: Any number raised to 0 = 1
Example 3: Any number raised to 1 = the same number (x^1 = x)
Example 4:x^a*x^b= x^a+b
(ONLY WHEN THE BASES ARE THE SAME, APPLIES TO MULTIPLICATION ONLY)

Distance Formula

Rate = distance/time

Example 1: 50 miles / 10 mph = (50/10) = 5 hours
Example 2: $50 for 5 CDs = (50/5) = $10 each
Example 3: 2000 ft in 5 seconds - (2000/5) = 400 ft per second
Example 4: 5 lbs potatoes for $4 = (5/4) = $1.25 per pound

Percents

Convert a decimal to a percent:
0.20 = .20 x 100 = 20%

Convert a percent to a decimal
20% = 20 / 100 = 0.20

Solve 20% of 400
1. 20% = 0.20
2. 0.20 x 400 = 80

Solve Percent Problems
5 out of 25 = 5/25 = .2 = 20%
5 out of 100 = 5/100 = .05 = 5%

Solve for x
1. x is 40% of 80 (convert percent to decimal and multiply)
2. x = .4 * 80
3. x = 32%

Proportions

Definition: 2 equal ratios.

Example 1:

2/4 = 8/16

-OR-

2:4 = 8:16

Cross products should always be equal. So in this example:
2 * 16 = 32 (extremes)
4 * 8 = 32 (means)

What if 16 was missing how would you find it?

2/4 = 8/?

Solve:

First multiple the cross products:
2 * x = 4 * 8
Then divide
2/2 = x
32/2 = 16

Ratios

Multiply or divide by the same number.

Example 1:

Find an equal ratio for 20:29

20 * 2 = 40
29 * 2 = 58

Answer: 40:58

Example 2:

Find an equal ratio for 22:14

22 / 2 = 11
14 / 2 = 7

11:7