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When there’s an election, the newspapers often write about the amount of support all the different parties have in an effort to give the readers an image of the political landscape. They might report that one party has the support of $30\phantom{\rule{0.17em}{0ex}}\text{\%}$ of the voters, and that this is an increase by $2.3$ percentage points compared to last month. When this percentage increases or decreases in the polls, you’re not given those changes in percentage change, but a change in percentage points. This works the same way as adding or subtracting with normal numbers, meaning that if a party with $30\phantom{\rule{0.17em}{0ex}}\text{\%}$ support gains $2.3$ percentage points, they now have $30\phantom{\rule{0.17em}{0ex}}\text{\%}+2.3\phantom{\rule{0.17em}{0ex}}\text{\%}=32.3\phantom{\rule{0.17em}{0ex}}\text{\%}$ support.

Theory

Percentage points describe the change of a number given in percentages, where the change follows the normal rules of adding and subtracting.

Example 1

A party becomes more popular in the polls, going from $4\phantom{\rule{0.17em}{0ex}}\text{\%}$ to $6\phantom{\rule{0.17em}{0ex}}\text{\%}$. That means the support of that party has increased by

$$6-4=2$$ |

percentage points. If you want to find the percentage change in support, you’ll find it to be $50\phantom{\rule{0.17em}{0ex}}\text{\%}$, because

$$\frac{6-4}{4}=\frac{2}{4}=0.5=50\phantom{\rule{0.17em}{0ex}}\text{\%}.$$ |

Example 2

**In a survey, $\text{}30.1\text{}\phantom{\rule{0.17em}{0ex}}\text{\%}$ of the population of Washington D.C. answers that they have used public transport as part of their commute at least once a week. Two years later, this has increased to $\text{}35.7\text{}\phantom{\rule{0.17em}{0ex}}\text{\%}$. That means that the number of people who use public transport as part of their commute has increased by **

$$\text{}35.7\text{}-\text{}30.1\text{}=\text{}5.6\text{}$$ |

percentage points in two years. What’s the growth in percentages?

Now you need to use the formula for percentage change:

$$\begin{array}{llll}\hfill & \frac{\text{newvalue}-\text{oldvalue}}{\text{oldvalue}}\cdot 100\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{2em}{0ex}}=\frac{5.6}{30.1}\cdot 100\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \phantom{\rule{2em}{0ex}}=18.6\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

$$\begin{array}{llll}\hfill \frac{\text{newvalue}-\text{oldvalue}}{\text{oldvalue}}\cdot 100\phantom{\rule{0.17em}{0ex}}\text{\%}& =\frac{5.6}{30.1}\cdot 100\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =18.6\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

You can see that the percentage change is $18.6\phantom{\rule{0.17em}{0ex}}\text{\%}$, while the change in percentage points is $5.6$.