🏷️ 百分数：每一百份里占几份🏷️ Percentages: How Many per Hundred
上一片里，比把两份量摆在一起看。这一片请出它的「标准版」：不管两份量具体是多少，都统一换算成「每一百份里占几份」——百分数。Last leaf, a ratio placed two amounts side by side. This leaf brings its “standard edition”: whatever the amounts, rescale them to “how many per hundred” — the percentage.
第 1 步：百分数 = 分母 100 的分数Step 1: A percentage is a fraction with denominator 100
先看商店的价签：75% 到底是什么意思？Start at the shop counter: what does 75% actually mean?
75% 读作「百分之七十五」，就是 75/100——分母固定为 100 的分数。写成小数是 0.75；200 元付 75% 就是 200×0.75 = 150 元。百分号「%」就是「除以 100」的记号：75% = 75 ÷ 100。75% reads “seventy-five percent” — that is 75/100, a fraction whose denominator is always 100. As a decimal it is 0.75; 75% of $200 is 200×0.75 = $150. The sign “%” simply means “divide by 100”: 75% = 75 ÷ 100.
那 30% 到底有多少？把整个格子切成 100 小格，一看便知。So how much is 30%? Cut the whole into 100 little squares and it becomes obvious.
第 2 步：百分格：100 格里亮几格Step 2: The hundred grid: how many of the 100 squares light up
一个 10×10 的方格正好 100 格：亮起 30 格就是 30%，亮起一半就是 50%。百分数把「一个整体里的几份」放上同一把尺子——不管整体多大，都换算成「100 份里占几份」，比较起来特别方便。A 10×10 grid is exactly 100 squares: 30 lit squares = 30%, half the grid lit = 50%. Percentages put every “part of a whole” on one ruler — out of 100 — so any two of them compare easily, no matter how big the whole is.
这把「统一尺子」在生活里到处都是——比如屏幕上这根进度条。That one ruler is everywhere in daily life — take the progress bar on a screen.
第 3 步：真实场景：进度条与及格线Step 3: Real world: progress bars and pass lines
下载进度 60%，意思是 100 份任务完成了 60 份；满分 100 分考 90 分就是 90%；60% 的及格线放到 150 分制就是 90 分（两边同乘 1.5）。百分数还常和比搭档：折扣就是现价占原价的百分之几。A download at 60% means 60 of every 100 parts are done; 90 out of 100 is 90%; and a 60% pass line on a 150-point paper is 90 points (both sides ×1.5). Percentages also team up with ratios: a discount is just the sale price as a percent of the list price.
🎮 你来当收银员（45 秒）🎮 Your turn: run the discount counter (45 seconds)
道理讲完了。拖动折扣滑块，把 4 件商品标到客人要的价钱——每一百份里付几份，一眼看清。Theory done. Drag the discount slider to tag all 4 items at the prices the guests want — see at a glance how many per hundred you pay.
一句话记住它：百分数 = 分母是 100 的分数，用「每一百份里占几份」这把统一的尺子丈量所有比例。Remember it in one line: a percentage is a fraction with denominator 100 — one ruler, “how many per hundred”, for every ratio.
75% = 75/100 = 0.75；「%」就是除以 10075% = 75/100 = 0.75; the “%” sign means divide by 100百分格：100 格里亮 30 格就是 30%The hundred grid: 30 lit squares out of 100 is 30%折扣、进度、及格线、涨薪……都是百分数Discounts, progress, pass lines, pay raises — all percentages
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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