一、the number of
1. 表示数量：即the number of表示“……的数量（指总数量）”，这是大家比较熟悉的用法：
There has been a steady decrease in the number of visitors. 访客数量逐渐减少。
We have managed to increase the number of patients treated. 我们已设法提高了收治病人的数量。
The birth rate is the number of births compared to the number of the people. 出生率是出生人数与人口总数之比。
The last ten years have seen a dramatic fall in the number of adoptions. 过去十年中收养孩子的人数明显减少了。
这类结构若用作主语，谓语动词用单数：
The number of people in the crowd was underestimated by 5,000. 这群人的总数被少估计了5 000 人。
The number of new cases of the illness appears to be declining. 这种病症的新发病例数量呈下降趋势。
The number of people with diabetes is growing, partly because of an increase in levels of obesity. 患糖尿病的人数不断上升，部分原因是肥胖人数增加。
2. 表示号码：即the number of表示“……的号码”。如：
What is the number of your latest requisition? 你最近一次订购单的号码是多少?
Slot told Natalie the number of his suite. 斯洛特把他套间的号码告诉了纳塔莉。
The policeman demanded the number of his driver’s license. 警察要他说出驾驶执照的号码。
I’ve marked down the number of each item sold. 卖出的每件东西的号码我都记下来了。
I can’t see the number of that bus without my glasses. 没戴眼镜我看不清楚那辆公共汽车的号码。
二、the numbers of
1. 表示数量：与the number of的用法相同，也是表示“……的数量（指总数量）”，有人说用复数的numbers语气更强调，但没有在相关权威资料上找到依据。如：
There was a rapid growth in the numbers of private cars. 私人汽车的数量增长很快。（牛津英语搭配词典）
There is a large increase in the numbers of young people going to college. 念大学的年轻人增加了不少。（牛津中阶词典）
Look at the numbers of small businesses that are being hammered unmercifully. 看看有多少小企业正在遭受无情的打击。（柯林斯词典）
The growing popularity of the subject is evident in the numbers of students wanting to study it. 从想修读的学生人数就可以明显看出这门课程越来越受欢迎。（朗文应试词典）
The numbers of people involved have been grossly inflated by the media. 涉及的人数被媒体严重辱大了。（朗文应试词典）
The last ten years have seen a twofold increase in the numbers of deaths on the road. 过去十年里死于道路交通事故的人数增加了一倍。（朗文英语写作词典）
The union is pressing for higher pay but has made no stipulations about the numbers of workers to be employed. 工会在努力争取提高薪酬，但没有明确规定应雇用多少工人。（朗文英语写作词典）
另外，若指多个群体各自的数量或同一群体在不同阶段的数量，则宜用the numbers of。如：
The numbers of visitors in different seasons vary greatly. 不同季节的游客数量差异很大。
比较下面两句：
The report highlights the decline in the number of native plants and insects. 报告强调当地植物及昆虫的数量有所减少。（用单数的number，指植物和昆虫的总数量）
The report highlights the decline in the numbers of native plants and insects. 报告强调当地植物及昆虫的数量有所减少。（用复数的number，指植物和昆虫各自的数量，相当于the number of native plants and the number of insects）
再比较下面两句：
The number of football players and basketball players in our school are constantly being swelled. 我校足球队和篮球队的队员在不断地增长。（用单数的number，指足球队和篮球队的总数量）
The numbers of football players and basketball players in our school are constantly being swelled. 我校足球队和篮球队的队员在不断地增长。（用复数的number，指足球队和篮球队各自的数量，相当于the number of football players and the number of basketball players）
注意，与the number of...作主语时要接单数动词不同，the numbers of...作主语时后面要接复数动词。如：
The numbers of the unemployed are still increasing. 失业人数还在增加。（《张道真英语用法》）
The numbers of people involved have been grossly inflated by the media. 涉及的人数被媒体严重夸大了。（《朗文考试词典》）
2. 表示号码：与the number of（表示“某个”事物的号码）不同，the numbers of通常表示“多个”事物各自的号码。如：
The numbers of the houses on this side of the street are even. 街道这边的房屋的门牌号是双数。（摘自L.G.Alexander的Right Word Wrong Word）
网友举2019年天津卷的例子也属类似用法（这里的number表示“数值”）：
To calculate biological age, Professor Levine at Yale University identified nine biomarker that seemed to be the most influential on lifespan by a simple blood test. The numbers of those markers, such as blood sugar and immune (免疫的) measures, can be put into the computer, and the algorithm (算式, 算法) does the rest. 为了计算生物年龄，耶鲁大学的莱文教授通过一项简单的血液检测，确定了九种似乎对寿命影响最大的生物标志物。这些标志物（各自）的数值（如血糖和免疫指标等）可输入电脑，其余工作则由算法完成。
