Understanding Percent and Its Calculations

Study Notes

Definition of Percent

Percent means "per hundred."
It is a way to express a number as a fraction of 100.

Symbol

Represented by the symbol "%".

Converting Percent to Decimal

Divide the percent value by 100.
- Example: 25% = 25/100 = 0.25

Converting Decimal to Percent

Multiply the decimal value by 100.
- Example: 0.75 = 0.75 × 100 = 75%

Calculating Percent of a Number

Use the formula:
- Percent × Whole Number = Part
Example: To find 20% of 50:
- 0.20 × 50 = 10

Finding the Whole from a Percent

Use the formula:
- Part = Percent × Whole Number
Rearranged to find Whole:
- Whole = Part / Percent
Example: If 30 is 15% of a number:
- Whole = 30 / 0.15 = 200

Percent Increase/Decrease

Percent Increase:
- Formula: ((New Value - Original Value) / Original Value) × 100
- Example: Going from 50 to 60: ((60 - 50) / 50) × 100 = 20%
Percent Decrease:
- Formula: ((Original Value - New Value) / Original Value) × 100
- Example: Going from 80 to 60: ((80 - 60) / 80) × 100 = 25%

Common Percent Values

10% = 0.10
20% = 0.20
25% = 0.25
50% = 0.50
75% = 0.75
100% = 1.00

Applications of Percent

Used in finance (interest rates, discounts).
Common in statistics (data representation).
Important in everyday calculations (tips, taxes).

Key Points to Remember

Always express percent as a fraction of 100.
Percent calculations can involve increases, decreases, and finding parts of a whole.
Understanding and converting between percent, decimal, and fractions is crucial in various applications.

Definition of Percent

Percent means "per hundred" and represents a number as a fraction of 100.
The symbol for percent is "%".

Converting Percent and Decimal

To convert a percent to a decimal, divide by 100 (e.g., 25% = 0.25).
To convert a decimal to a percent, multiply by 100 (e.g., 0.75 = 75%).

Calculating Percent of a Number

Use the formula: Percent × Whole Number = Part.
For instance, to find 20% of 50, calculate 0.20 × 50 = 10.

Finding the Whole from a Percent

To determine the whole when given a part and percent, rearrange the formula: Whole = Part / Percent.
Example: If 30 is 15% of a number, calculate Whole = 30 / 0.15 = 200.

Percent Increase and Decrease

Percent Increase: Calculate using the formula: ((New Value - Original Value) / Original Value) × 100. Example: From 50 to 60 yields a 20% increase.
Percent Decrease: Use the formula: ((Original Value - New Value) / Original Value) × 100. Example: From 80 to 60 results in a 25% decrease.

Common Percent Values

Recognize these key conversions: 10% equals 0.10, 20% equals 0.20, 25% equals 0.25, 50% equals 0.50, 75% equals 0.75, and 100% equals 1.00.

Applications of Percent

Percentages are commonly used in finance (e.g., interest rates and discounts), statistics (for data representation), and everyday calculations (like tips and taxes).

Key Points to Remember

Always express percent as a fraction out of 100.
Percent calculations cover increases, decreases, and finding parts of whole numbers.
Proficiency in converting between percent, decimal, and fractions is essential for various practical applications.

Description

This quiz covers the definition of percent, its symbol, and how to convert between percent and decimal values. You'll also learn how to calculate the percent of a number and find whole values from a given percent. Additionally, the quiz explores percent increase and decrease with examples.