Unit 2 · Topic 01 · Comparing Quantities
Kabir scored 18 out of 25 on a quiz and Zara scored 21 out of 28 on a different one. He insisted he'd done better since 21 is a bigger number than 18.
Zara said the totals were different, so the raw scores couldn't be compared directly.
She converted both to percentages, and the winner surprised him.
Kabir and Zara compared quiz results after class. Kabir got 18 out of 25, Zara got 21 out of 28. "21 beats 18," Kabir said. "I win." Zara pointed out the quizzes weren't out of the same total, so the raw numbers meant nothing on their own — they needed a common scale.
"That's what percent is for," she said. "Percent means 'out of 100'. If we convert both scores to a mark out of 100, we can compare them fairly." She wrote 18/25 and multiplied top and bottom by 4 to get 72/100, which is 72%. Then she wrote 21/28, simplified it to 3/4, and multiplied by 100 to get 75%.
"75 beats 72," she said. "I actually did better, even though 21 looks bigger than 18 as a raw number." Kabir checked her method: to convert any fraction to a percent, multiply the fraction by 100 and attach a percent sign. 18/25 × 100 = 72%. He tried it on 3/5: 3/5 × 100 = 60%.
Zara showed him the reverse direction too: converting a percent back to a fraction or decimal. 45% means 45/100, which simplifies to 9/20 as a fraction, or 0.45 as a decimal — just move the decimal point two places left. Kabir tested this on 6%, getting 0.06, and on 130%, getting 1.3, confirming that percentages above 100% are perfectly valid and just mean more than the whole.
"So decimal, fraction, and percent are three ways of writing the exact same amount," Kabir said. "They're not different kinds of number, just different notations." Zara agreed, and showed him a quick table: 1/4 = 0.25 = 25%, 1/2 = 0.5 = 50%, 3/4 = 0.75 = 75% — worth memorising since they come up constantly.
By the end, Kabir had stopped comparing raw scores out of different totals altogether. "Percent puts everything on the same 100-point scale," he said, "so comparisons are actually fair."
Percent means 'per hundred' — a percentage is a fraction with denominator 100, written with a % sign instead of /100.
To convert a fraction to a percent: multiply the fraction by 100 and attach %. To convert a decimal to a percent: multiply by 100 (shift the decimal point two places right) and attach %.
To convert a percent to a fraction: write it over 100 and simplify. To convert a percent to a decimal: divide by 100 (shift the decimal point two places left).
Percentages can exceed 100% (meaning more than the whole) and comparing two quantities out of different totals is only fair once both are converted to the same percent scale.
Convert 17/20 and 23/25 to percentages and decide which is larger, without simplifying first.
Write 0.6, 0.06, and 6 as percentages, and notice how the decimal point shift changes each result.
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