这部分需要会什么？
- 将百分数、小数和分数互换
- 识别百分比关系中的比较基准
- 根据部分量、整体量和比例中的两个求第三个
核心概念与公式
\(p\%=p/100\)。若 A 是 B 的 \(p\%\)，则 \(A=(p/100)B\)。B 是比较基准；要求 A 是 B 的百分之几，应计算 \(A/B\times100\%\)，前提是 \(B\ne0\)。
如果题目问“\(p\) 的值”且写作 \(p\%\)，最终通常填写百分数前的数，例如 25；如果问对应的小数比例，则为 0.25。应按题目的表达方式作答。
做题时怎样使用
- 圈出“谁的百分之几”，确定整体或比较对象
- 写出“部分量 = 比例 × 基准量”
- 求百分数时先求比值再乘 100，并检查答案的形式
容易混淆的地方
“A 是 B 的 120%”表示 \(A=1.2B\)；“A 比 B 多 120%”表示 \(A=2.2B\)。两句话不同。
用一个例题串起方法
知识点教学例题某班有 40 人，其中 14 人选择某门选修课。选择人数占全班的百分之几？
展开解题思路 ＋
以全班 40 人为基准，比例为 \(14/40=0.35\)，所以占 \(35\%\)。若题目要求 \(p\) 的值，则填写 35。
本知识点题库
先独立作答，再查看答案与解析。
百分比关系・求百分数挑战
The positive number a is 2106% of the sum of the positive numbers b and c, and b is 81% of c. What percent of b is a?
原库参考解析
百分比关系・求百分数挑战
A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed was 7,150% of the number of postdoctoral students surveyed and the number of graduate students surveyed was 45% of the number of undergraduate students surveyed. If there were 6,435 graduate students surveyed, what was the sum of the number of undergraduate students and postdoctoral students surveyed?
原库参考解析
百分比关系・求百分数挑战
If 350% of n is 35, what is the value of n?
原库参考解析
百分比关系・求百分数挑战
The mass of object \( A \) is \( 484\% \) of the mass of object \( B \), and the mass of object \( A \) is 0.880% of the mass of object \( C \). If the mass of object is \( p\% \) of the mass of object \( B \), what is the value of \( p \)?
原库参考解析
百分比关系・求百分数进阶
In 1980, the population density of Carroll County was 125 people per square mile. In 1990, the population density of Carroll County was 141 people per square mile. The population density of Carroll County in 1990 was \( p\% \) of the population density of Carroll County in 1980. What is the value of \( p \)?
原库参考解析
百分比关系・求百分数进阶
The table summarizes the number of objects in each group.
The number of objects in group C is p% of the number of objects in group A. What is the value of p?
原库参考解析
百分比关系・求百分数进阶
While the mass of an object is the same everywhere, the weight of an object is not the same on different planets. An object has a weight of 170.00 pounds on Earth and a weight of 186.32 pounds on Neptune. The object’s weight on Jupiter is 252.8% of its weight on Earth. If the object’s weight on Neptune is x% of its weight on Jupiter, which of the following is closest to the value of x?
原库参考解析
百分比关系・求百分数挑战
A scientist analyzed a soil sample with a mass of 900 grams and determined that it contained 189 grams of water. What is the percentage of water, by mass, in this soil sample?
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百分比关系・求百分数进阶
An entomologist placed an initial population of 40 Tenebrio molitor, a type of beetle, into a habitat and monitored the population over time. When the number of Tenebrio molitor in the habitat reached 170% of the initial population, the entomologist moved 75% of the Tenebrio molitor to a second habitat. How many Tenebrio molitor did the entomologist move to the second habitat at this time?
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百分比关系・求百分数挑战
On a plot of land, 48.0% of the square footage is farmland and the remaining square footage is pasture. There are buildings on exactly 23.5% of the square footage of the farmland, and there are buildings on exactly 16.0% of the square footage of the pasture. If there are buildings on exactly p% of the square footage of the plot of land, what is the value of p?
原库参考解析
百分比关系・求百分数进阶
There are 350 objects in a bag. Of these objects, 4% are spheres. How many spheres are in the bag?
原库参考解析
百分比关系・求百分数挑战
On a plot of land, 52.0% of the square footage is farmland and the remaining square footage is pasture. There are buildings on exactly 28.5% of the square footage of the farmland, and there are buildings on exactly 11.0% of the square footage of the pasture. If there are buildings on exactly p% of the square footage of the plot of land, what is the value of p?
原库参考解析
