### 有理数 Rational Number

#### 1 英语原意

有理数 rational number

#### 2 rational number 英语原意

A Rational Number can be made by dividing an integer by an integer.

Example:

1.5 is a rational number because 1.5 = 3/2 (3 and 2 are both integers)

Here are some more examples:

Number | As a Fraction | Rational? |
---|---|---|

5 | 5/1 | Yes |

1.75 | 7/4 | Yes |

1000 | 1000/1 | Yes |

0.001 | 1/1000 | Yes |

−0.1 | -1/10 | Yes |

0.111... | 1/9 | yes |

√2 (square root of 2) | ? | No! |

Oops! The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they are not rational they are called Irrational.

Another famous irrational number is Pi (π)

Formal Definition of Rational Number

More formally we say:

A rational number is a number that can be in the form p/q

where p and q are integers and q is not equal to zero.

So, a rational number can be: p/q

where q is not zero.

#### 3 Rational、Ratio和 Rate 的含义

rational adjective

based on clear thought and reason:

Examples：

- There must be some rational explanation for what happened.
- a rational act/course of action
- a rational argument/decision
- He was too upset to be rational.

**Ratio noun**

**the relationship between two groups or amounts that expresses how much bigger one is than the other:**

- The ratio of men to women at the conference was ten to one/10:1.
- The school is trying to improve its pupil-teacher ratio (= the number of teachers compared with the number of students).

Rate

rate noun [C] (MEASURE)

the speed at which something happens or changes, or the amount or number of times it happens or changes in a particular period:

- Although she's recovering from her illness, her rate of progress is quite slow.
- I told my assistants to work at their own rate.
- The taxi was going at a tremendous rate.
- the growth/inflation/mortality/unemployment, etc. rate
- The drug has a high success/failure rate.

rate noun [C] (PAYMENT)

an amount or level of payment:

- We agreed a rate with the painter before he started work.
- What's the going (= standard) rate for this type of work?
- Do you pay your mortgage on a fixed or variable rate (= of interest)?

rate noun [C] (TAX)

a local tax paid in Australia, and in Britain in the past, by the owners of houses and other buildings:

- I see rates are going up again.

rate verb [T] (JUDGE)

to judge the value or character of someone or something:

- How do you rate him as a football player?
- She is rated very highly by the people she works for.
- informal "What do you think of her as a singer?" "I don't really rate her (= I do not think that she is very good)."
- I rate cars as one of the worst polluters of the environment.
- On a scale of one to ten, I'd rate his book a five.
- Traffic accidents are so frequent that they don't rate a mention (= are not considered to be worth reporting) in the newspaper unless a lot of people are killed.

rate verb [T] (TAX)

- In Britain in the past, a building was rated to decide how much local tax the owner should pay.

#### 3 中文含义

有理数是整数（正整数、0、负整数）和分数的统称，是整数和分数的集合。

#### 4 感想

“有理数”这一名称不免叫人费解，有理数并不比别的数更“有道理”。事实上，这似乎是一个翻译上的失误。有理数一词是从西方传来，在英语中是rational number，而rational通常的意义是“理性的”。中国在近代翻译西方科学著作，依据日语中的翻译方法，以讹传讹，把它译成了“有理数”。但是，这个词来源于古希腊，其英文词根为ratio，就是比率的意思（这里的词根是英语中的，希腊语意义与之相同）。所以这个词的意义也很显豁，就是整数的“比”。与之相对，“无理数”就是不能精确表示为两个整数之比的数，而并非没有道理。

参考文献：

- https://dictionary.cambridge.org/dictionary/english/rational
- https://www.mathsisfun.com/rational-numbers.html

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