What is a Percentage?

A percentage is a mathematical way to express a number or ratio as a fraction of 100. It provides a dimensionless relationship between two values, similar to ratios, fractions, and decimals. The term “percent” comes from the Latin per centum, meaning “by the hundred.”

Percentages are denoted using the symbol “%” (e.g., 35%) or the words “percent” or “pct” (e.g., 35 percent). For example:

• 35% is equivalent to the decimal 0.35 or the fraction 35/100.

Calculating a Percentage

To find a percentage, multiply the value of a ratio by 100. For instance:

• If 25 out of 50 students in a class are male, the ratio is 25/50 = 0.5.
• Multiplying by 100 gives: 0.5 × 100 = 50%.

This means 50% of the students in the classroom are male.

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Percentage Formula

The percentage formula is an algebraic equation involving three values:

P × V₁ = V₂

Where:

• P = Percentage (in decimal form)
• V₁ = Initial value
• V₂ = Result after applying the percentage

Example:
If P × 30 = 1.5, then:P=1.530=0.05P=301.5​=0.05

Convert to a percentage by multiplying by 100:0.05×100=5%0.05×100=5%

When solving manually, the decimal form of the percentage must be converted back to a percent by multiplying by 100.

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Percentage Difference Formula

The percentage difference between two values measures their relative difference. It is calculated as:Percentage Difference=∣V1−V2∣(V1+V2)/2×100Percentage Difference=(V1​+V2​)/2∣V1​−V2​∣​×100

Example:
For values 10 and 6:∣10−6∣(10+6)/2=48=0.5=50%(10+6)/2∣10−6∣​=84​=0.5=50%

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Percentage Change Formula

The percentage change calculates how much a value increases or decreases relative to its original amount.Percentage Change=New Value−Original ValueOriginal Value×100Percentage Change=Original ValueNew Value−Original Value​×100

Examples:

Decrease: If 500 drops by 10% (0.1):500× 1−0.1 450500×(1−0.1)=450

Increase: If 500 grows by 10% (0.1):500× 1+0.1 550500×(1+0.1)=550