Calculating Percentages

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. It means "per hundred". For example, 25\% means 25 out of every 100, or 25 parts of 100.

Percentages are useful in geography to compare data easily, such as population growth, land use, or survey results.

You can convert between fractions, decimals, and percentages:

• To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100.
• To convert a decimal to a percentage, multiply the decimal by 100.
• To convert a percentage to a decimal, divide by 100.
• To convert a percentage to a fraction, write the percentage over 100 and simplify if possible.

For instance, to convert the fraction $\frac{3}{5}$ to a percentage:

$$\frac{3}{5} = 0.6$$

Multiply by 100:

$0.6 \times 100 = 60\%$

Calculating Percentages

Calculating percentages is essential for interpreting data in geography. Here are the main skills:

Finding a Percentage of a Quantity

To find a percentage of a quantity, multiply the quantity by the percentage (as a decimal).

Formula:
$$\text{Percentage of quantity} = \text{Quantity} \times \frac{\text{Percentage}}{100}$$

For example, if a town has 12,000 people and $25\%$ are under 16 years old, the number of young people is:

$12,000 \times \frac{25}{100} = 12,000 \times 0.25 = 3,000$

Calculating Percentage Increase or Decrease

Percentage change shows how much a value has increased or decreased compared to its original amount.

Formula:
$$\text{Percentage change} = \frac{\text{Change in value}}{\text{Original value}} \times 100\%$$

Where:

• Change in value = New value − Original value
• If the result is positive, it's a percentage increase.
• If the result is negative, it's a percentage decrease.

For example, if a city’s population grew from 50,000 to 55,000:

Change = $55,000 - 50,000 = 5,000$

Percentage increase = $\frac{5,000}{50,000} \times 100 = 10\%$

Using Percentages in Data Interpretation

Percentages help compare data from different places or times, even if the total amounts differ. For example, comparing unemployment rates between two towns is easier using percentages rather than raw numbers.

Always check what the percentage is of, and be careful to interpret it correctly in context.

Applying Percentages to Graphs

Graphs often show data in percentages to make it easier to understand proportions and comparisons.

Interpreting Pie Charts with Percentages

Pie charts display data as slices of a circle, where each slice represents a percentage of the whole.

To interpret a pie chart:

• Check the percentage for each slice.
• Understand what the whole pie represents (e.g., total population, total land area).
• Use the percentages to compare categories easily.

For example, if a pie chart shows land use with $40\%$ farmland, $30\%$ forest, and $30\%$ urban, you know farmland covers the largest area.

Using Percentages in Bar Charts

Bar charts can show percentages on the vertical axis to compare categories.

For example, a bar chart might show the percentage of people in different age groups in a city. The height of each bar corresponds to the percentage.

You can calculate exact values from percentages if you know the total.

Calculating Proportions from Graphs

Sometimes you need to find the actual number from a percentage shown on a graph.

Use the formula:

$$\text{Actual number} = \text{Total} \times \frac{\text{Percentage}}{100}$$

For example, if a bar chart shows $15\%$ of people in a town are unemployed and the total population is 20,000, the number unemployed is:

$20,000 \times \frac{15}{100} = 3,000$

Example: A survey shows that $60\%$ of people in a village use public transport. If the village population is 5,000, how many people use public transport?

Calculate:

$5,000 \times \frac{60}{100} = 3,000$ people use public transport.