Percentage in Practice: Discounts, Increases and Everyday Comparisons

The word 'percentage' comes from the Latin 'per centum', meaning 'per hundred' or 'for every hundred'. When we say something costs 30% more, we mean that for every 100 units of the original value, 30 extra units are added. This idea of 'parts per hundred' is the core of every percentage calculation.

In practice, percentage is a way to express a proportion with a fixed base of 100. That is why it is so useful for comparing different quantities: if one product has a 15% discount and another has 20%, the comparison is immediate — regardless of each product's original price. The same language works equally well for comparing supermarket prices and understanding inflation figures in the news.

There is a direct relationship between percentage, fraction, and decimal. The value 25% equals the fraction 25/100, which simplifies to 1/4, and the decimal 0.25. Moving fluently between these three forms is essential: the decimal form is the most practical for calculator use, the fractional form helps visualise proportions, and the percentage form is the most common in everyday communication.

The most straightforward way to calculate a percentage of any value is to convert the percentage to a decimal and multiply it by the base value. The conversion is simple: divide the percentage number by 100. So 18% becomes 0.18; 7.5% becomes 0.075; 120% becomes 1.20.

Practical example: a smartphone costs $1,200 and is 12% off. How much do you save? Calculate 0.12 × 1,200 = 144. The discount is $144, and the final price is $1,056. Notice you can also calculate the final price directly: since there is a 12% discount, you pay 88% of the original, so 0.88 × 1,200 = 1,056.

Another common calculation is finding what percentage one value represents of another. If you earned $350 and paid $70 in taxes, what percentage was taken? Divide 70 by 350 and multiply by 100: (70/350) × 100 = 20%.

When you see a tag that says '40% off', many people instinctively think 'I'll pay 40% of the price'. Wrong — you pay 60% of the original price, because you are saving 40%. To calculate the final price, multiply the original value by 0.60.

Promotions with stacked discounts deserve special attention. If a store offers '30% off + extra 10%', the total discount is not 40%. First, 30% off is applied: 70% of the price remains. Over that new value, an extra 10% off is applied, leaving 90% of the 70%. The calculation is 0.70 × 0.90 = 0.63 — you pay 63% of the original price, and the total discount is 37%, not 40%.

In e-commerce, always compare final prices, not just discount percentages. A product with 50% off can still be more expensive than one with 20% off if the original prices differ significantly.

A percentage increase works analogously to a discount, but in the opposite direction. If your $3,000 salary was raised by 8%, your new salary is $3,000 × 1.08 = $3,240. The additional $240 may seem small, but over 12 months it amounts to $2,880 more per year.

When following inflation news, we are dealing with accumulated percentage increases. If inflation was 5% in one year and 6% the next, the total accumulated increase is not 11%, but rather 1.05 × 1.06 = 1.113 — equivalent to an 11.3% increase over two years.

In personal finance, understanding percentage increases helps determine whether a salary raise outpaces the period's inflation. If your salary increased by 6% but inflation was 8%, your purchasing power actually decreased — you became poorer in real terms even though you received a nominal raise.

The most common percentage mistake is adding and subtracting percentages from different bases as if they shared the same base. A product that increases by 20% and then decreases by 20% does not return to its original price. Rising by 20%: multiply by 1.20. Falling by 20%: multiply by 0.80. The result is 1.20 × 0.80 = 0.96 — the product ends up 4% cheaper than it started.

Another frequent error is confusing 'percentage points' with 'percentage'. If an interest rate goes from 10% to 12%, it increased by 2 percentage points, but the percentage increase was 20% (because 2 is 20% of 10). This distinction is widely used in financial journalism.