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- In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It represented by the
**symbol “%”**. - Percentages have
**no dimension**. Hence it is called a dimensionless number. - Percentages can also be represented in
**decimal or fraction form**, such as 0.6%, 0.25%, etc.

**Important Formulas**

- Percent implies “for every hundred” - % is read as a percentage and x % is read as x per cent.
- To calculate:
- p % of y = (p/100) * y =
**(p * y)/100** - p % of y =
**y % of p**

- p % of y = (p/100) * y =
- To find what percentage of x is
**y: y/x * 100** - To calculate percentage change in value
- Percentage change =
**{change/(initial value)} x 100**

- Percentage change =
- Percentage point change = Difference of two percentage figures
- Increase N by S
**% = N( 1+ S/100 )** - Decrease N by S
**% = N (1 – S/100)** - If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original point is
**100x/ (100 + x) %.** - If A is x% more /less than B, then B is
**100x/(100 + x) %**less/more than A. - If the price of an item goes up/down by x %, then the quantity consumed should be reduced by
**100x/ (100 + x)%**so that the total expenditure remains the same. **Successive Percentage Change**- If there are successive percentage increases of a % and b%, the effective percentage increase is:
**{(a + b + (ab/100)}%**

- If there are successive percentage increases of a % and b%, the effective percentage increase is:

12. **Percentage – Ratio Equivalence**

**Table:** Fractions and their percentage equivalents:

**Percentage Tips**

- r% change can be nullified by (100r/100 + r)% change in another direction.
Example: An increase of 25% in prices can be nullified by a reduction of [100 x 25/(100 + 25)] = 20% reduction in consumption.- If a number ‘x’ is successively changed by a%, b%, c%...

⇒ Final value =- The net change after two successive changes of a% and b% is:

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