Learn: Percentages

Welcome!Today, we'll explore percentages and how to work with them in various scenarios. Percentages are a way to express numbers as parts of 100, and they are very useful in everyday life, like working out discounts, interest rates, or proportions. Ready to dive in?

What are Percentages?A percentage is a fraction or ratio expressed as a part of 100. Percentages are commonly used in financial calculations, statistics, and everyday situations, like finding discounts.For example, 25% means 25 out of 100, or 25 divided by 100, which is 0.25.

Converting Percentages to DecimalsTo convert a percentage to a decimal, divide the percentage by 100. For example, 25% becomes 0.25 because 25 ÷ 100 = 0.25.Percentages are often used to make calculations easier, especially when working with fractions.

Converting Decimals to PercentagesTo convert a decimal to a percentage, multiply the decimal by 100 and add the '%' symbol. For example, 0.75 becomes 75% because 0.75 × 100 = 75.This is useful when you want to express a ratio or proportion in terms of percentages.

Finding Percentages of a NumberTo find a percentage of a number, multiply the number by the percentage written as a decimal. For example, to find 20% of 50, calculate 50 × 0.20 = 10.This is useful for calculating discounts, tax, or interest.

Finding Percentage ChangePercentage change shows how much a value increases or decreases compared to its original amount. Use this formula:Percentage change = \frac{\text{Change in value}}{\text{Original value}} \times 100For example, if the price of an item goes from £50 to £60, the change is £10, and the percentage change is (10 ÷ 50) × 100 = 20% increase.

Reverse PercentagesReverse percentages are used to find the original amount before a percentage increase or decrease. To find the original value, divide the final amount by (1 ± percentage change as a decimal).For example, if the price after a 20% increase is £60, the original price is £60 ÷ 1.20 = £50.

Compound InterestCompound interest is interest calculated on the initial principal and also on the accumulated interest from previous periods. It can be calculated using the formula:A = P(1 + r)^nWhere A is the total amount, P is the principal, r is the interest rate (as a decimal), and n is the number of time periods.

Review Time!Great work! You've learned about percentages, how to calculate them, and their applications. Let's test your understanding with a few final questions.