**1. Percent**

The symbol for percent is %.

The fraction 1/100 is written for %

So, 50% is 50 × 1/100 = 50/100 = ½

**2. Formulas on Percent Change:**

*1. Percent Increase is *(amount of increase/initial number) × 100%

*2. Percent Decrease is *(amount of decrease/initial number) × 100%

**3. Formulas on Percent Comparison:**

*1. Percent Greater (more) is *(difference of the numbers)/(smaller number) × 100%

*2. Percent Smaller (less) is *(difference of the numbers)/(greater number) × 100%

**4. Formulas on Percent (total) change during successive percent changes:**

Note: In the following, + sign denotes increase, and – sign, decrease.

*1. If a number N is increased first by x% and next by y%, then the total percent **change is*

(x + y + (x y/100))%

*2. If a number N is decreased first by x% and increased next by y%, then the total percent **change is*

(- x + y – x y/100)%

*3. If a number N is increased first by x% and decreased next by y%, then the total percent **change is*

(+x – y –xy/100)%

**5. Formulas on Three important concepts on percents:**

*1. Consider a number N.*

It is successively increased twice by x% each time.

Then, the total percent increase is > 2x%

*2. Consider a Number N.*

It is successively decreased twice by x% each time.

Then, the total percent decrease is < 2x%

*3. Consider a Number N.*

It is successively increased and decreased by x% each time.

Then, the final value is less than the original value.