When a number is increased or decreased, then percentage change in the number is defined as \[\left[ {\frac{{{\rm{final}}\;\,{\rm{value}} - {\rm{initial}}\,\;{\rm{value}}}}{{{\rm{intial}}\,\;{\rm{value}}}}} \right] \times \,100\]For example, if a number increases from 35 to 50 the percentage change 

\( = \frac{{50 - 35}}{{35}} \times 100\,\, = \frac{{15}}{{35}} \times 100\,\, = \frac{3}{7} \times 100 = 42.85\% \) 

PERCENTAGE CHANGE AND THE EQUIVALENT FRACTIONS

If the \( \uparrow \) indicates increase and the \( \downarrow \) indicates decrease then, 

10% \( \uparrow \) Means number becomes 1.1 times

20% \( \uparrow \) Means number becomes 1.2 times 

15% \( \downarrow \) Means number becomes 0.85 times

In general an increment of \(x\%\) means number becomes \(\left( {1 + \frac{x}{{100}}} \right)\) times and a decrement of \(x\%\) means number becomes \(\left( {1 - \frac{x}{{100}}} \right)\) times.

PERCENTAGE POINTS 

Percentage point is used to simplify the data in percentage. Percentage point is defined as difference of two percentage figures for example if a man spends 10% of his salary in the month of January and 25% in the month of February, then we can say that expenditure increases by 15 percentage point.

Here note that percentage change in the expenditure is not 15, it is

\(\frac{{25 - 10}}{{10}} \times 100 = 150\% \) (Assuming that his salary remains constant)