A percentage in Mathematics is a number or ratio that is represented as a fraction of 100. The word ‘percent’ is derived from the Latin word ‘per centum’ which means “by a hundred”. Percentage is denoted by the symbol ‘%’. It is a dimensionless number and has no units.
Percentage basically means a part per hundred. It can be expressed in fraction form as well as decimal form.
For example, if we say 25%, it means 25 out of 100.
So, 25% is equivalent to the fraction 25/100 or 0.4 in decimal form.
Here are some examples of percentages.
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10% is equivalent to 10/100 or 0.1
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20% is equivalent to 20/100 or 0.2
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25% is equivalent to 25/100 or 0.25
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50% is equivalent to 50/100 or 0.5
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75% is equivalent to 75/100 or 0.75
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90% is equivalent to 90/100 or 0.9
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100% is equivalent to 100/100 or 1
Percentage Formula:
The basic formula used to calculate the percentage is equivalent to the ratio of actual value to the complete value multiplied by 100. The formula of the percentages is expressed as:
Percentage formula = \((\frac{Actual\, value}{Total\, value}) \times100\)
For Example: 2/4 × 100 = 0.5 × 100 = 50%
Percentage Difference Formula:
The percentage difference can be understood as the change in the value of an amount over some time in terms of percentage. If there are two values and we need to determine the percentage difference between the given two values, then this can be calculated by the below steps:
Step 1: Compute the difference (i.e subtract one value from the other) skip any negative sign if obtained.
Step 2: Estimate the average of the two values (add the values, then divide by 2).
Step 3: Finally divide the difference by the average obtained.
Step 4: Transform the obtained answer to a percentage for the result to be in percentages
Percentage Difference Formula = \(|\frac{First\, Value - Second\, Value}{(\frac{First\, Value + Second\, Value}{2})}| \times 100\%\)
The modulus symbols represent absolute value so that any negative outcome becomes positive.
Percentage Increase and Decrease Formula:
Two cases might appear while computing percentage difference namely:
(i) Percentage increase.
(ii) Percentage decrease.
The percentage increase is equivalent to subtracting the original number from the new number and dividing the obtained answer by the original number. Multiply the final answer by 100 for the answer to be in percentage.
Percentage Increase = \(\frac{Rise\, in\, the \, Number}{Original\, Number} \times 100\%\)
Rise in the Value = New number – Original number
Likewise, percentage decrease is comparable to subtracting the new number from the original numeral and dividing the obtained answer by the original number. Multiply the final answer by 100 for the answer to be in percentage.
Percentage Decrease = \(\frac{Decrease\, in\, the \, Number}{Original\, Number} \times 100\%\)
Decrease in the Number = Original number – New number
We should remember that when the new value/number is greater than the old number/value, it is a percentage increase, otherwise, it is a decreasing percentage.
Percentage Formula in terms of a Fraction:
To transform a fraction into a percentage divide the top/numerator number by the bottom/denominator number and lastly multiply the result by 100%.
\(\frac{Numerator\, Value}{Denominator\, Value} \times 100\%\)
Percentage Change Formula:
Sometimes when it is required to get the increase or decrease in any quantity as percentages, which is also directed to as percentage change is given by the formula:
Percentage Change = \(\frac{New\, value - Original\, value}{Original\, value} \times 100\)
To calculate the percentage of a number.
To calculate the percentage of a number, we need to use a different formula such as:
P% of Number = x
where x is the required percentage.
If we remove the % sign, then we need to express the above formulas as;
P/100 * Number = x
Example: Calculate 10% of 80.
Let 10% of 80 = x
10/100 x 80 = x
x = 8
