数学符号的英文表达
一、小数、分数、百分数
1. 小数表示法
小数点左边的数通常按基数词读，若为三位以上的数，也可按编码式读法读出，即将数字单个读出；小数点右边的数通常按编码式读法单个读出。如：
6.86 six point eight six
14.15 fourteen point one five
345.456 three four five point four five six 或 three hundred and forty－five point four five six
小数中“0”的读法：
“0”在小数中通常读作nought(英)或zero(美)，也可读作字母o。如：
0.08 (nought) point nought eight 或 (zero) point zero eight
9.07 nine point o seven
2. 百分数表示法
百分数中的百分号%读作percent。如：
6% 读作 six percent
0.6% 读作 (nought) point six percent
500% 读作 five hundred percent
3. 倍数表示法
倍数表示方法很多，如：
This room is four times as big as mine. 这个房间是我的房间的四倍。
This room is three times larger than mine. 这个房间比我的房间大二倍/是三倍。
The output of coal has doubled. 煤的产量增加了一倍。
My aunt is as old again as I am. 我姑姑年龄比我大一倍。
Productivity is increased three fold. 生产效率提高了两倍。
The volume of the Sun is about 1,300,000 times that of the Earth. 太阳的体积约为地球的1300000倍。
4. 分数表示法
(1) 较小分数的一般读写方法。如：
1/3 one-third
2/3 two-thirds
3/5 three-fifths
(2) 较复杂分数的简明读写方法。如：
22/9 twenty-two over nine
a/b a over b 或 a divided by b
43/97 forty-three over ninety-seven
(3) 整数与分数之间须用and连接。如：
four and a half nine and two fifths
(4) 分数用作前置定语时，分母要用单数形式。注意下列写法与读法。如：
a one-third mile 1/3英里
a three-quarter majority 3/4的多数
二、加、减、乘、除表示法
1．加：用 and, plus, added to 等词表示。
2＋4＝6 可译为：
Two and four is six.
Two plus four is equal to six.
Two added to four equals six.
Two and four makes six.
Two plus four will be six.
If you add two to four, you get six.
2．减：用 minus, taken from, subtracted from 等表示。
8－3=5可译为：
Eight minus three is five.
Eight minus three is equal to five.
Three taken from eight leaves five.
Three subtracted from eight leaves five.
Take three from eight and the remainder is five.
3．乘：用 multiply...by... / multiplied by / time 等表示。
3×5=15可译为：
Multiply three by five is(gives) fifteen.
Three multiplied by five is fifteen.
Multiply three by five, you get fifteen.
Three times five is (makes, will be, equals, is equal to) fifteen.
4．除：用 divide...by... / divided by / divide...into... / into 等表示。
24÷8=3 可译为：
Twenty-four divided by eight makes(is, equals) three.
Twenty-four divided by eight is equal to three.
Eight into twenty-four goes three times.
Divide eight into twenty-four, and you get three.
Divide twenty-four by eight, and you get three.
小结：
6+5＝11 Six plus five is eleven ./Six and five is eleven.
11-6＝5 Eleven minus six is five. /Six from eleven is five.
4×5＝20 Four multiplied by five is twenty./Four times five is twenty.
20÷4＝5 Twenty divided by four is five./Four into twenty goes five.
15:5＝3 The ratio of fifteen to five is three.
其他补充：
3的平方=9 Three squared/square is nine./The second power of 3 is 9./The square of 3 is 9./5 to the second power is 9.
2的立方=8 Two cubed is eight./......
16的-4次方=2 16 to the (power) minus 4 is 2./
2的4次方=16 The fourth power of two is sixteen./Two to the power 4 is sixteen.
X^(1/2)=Y The square root of X is Y.
X^(1/3)=Y The cubic root of X is Y.
X^(1/4)=Y The forth root of X is Y./X to the power of one over four.
a > b a is more/greater than b.
a>>b a is much greater than b.
a < b a is less than b.
a ≈ b a approximately equals to/is approximately equal to b.
a ≠ b a is not equal to b.
a ≡ b a is identically equal to b.
( ) round brackets/parentheses.
[ ] square brackets/angular brackets.
{ } braces.
|X| the absolute value of X.
(a-b-c×d)/e=f a plus b minus c multiplied by d, all divided by e equals f.
三、英语中倍数关系表达式
1）n times +形容词（或副词）比较级+than…
times是用来表示“乘”的（used to indicate multiplication）n times就是“乘以n”的意思。不论在任何句型中都包括基数100%在内。
[1] Asia is four times larger than Europe.
误译：亚洲比欧洲大4倍。
正译：亚洲比欧洲大3倍。
评析：亚洲面积4400万平方公里，欧洲面积1016万平方公里。因此亚洲应该是欧洲面积的四倍，即亚洲比欧洲大3倍。
[2] Sound travels nearly 3 times faster in copper than in lead.
声音在铜中的传播速度几乎比在铅中快2倍。
评析：声音在铜中的传播速度为2100m/s，在铅中在的传播速度为710m/s，可见声音在铜中的传播速度几乎是铅中的3倍，而不是比铅快3倍。
[3] The volume of the earth is 49 times larger than that of the moon.
地球的大小是月球的49倍。
或：地球比月球大48倍。
2) n times +形容词（或副词）原级+as
[4] The oxygen atom is nearly 16 times as heavy as the hydrogen atom.
氧原子的重量几乎是氢原子的16倍。
评析：经查，氧原子的重量为15.9994，氢原子量为1。
[5] The mercury atom is about 5 times as heavy as calcium atom.
汞的原子重量大约为钙的5倍。
评析：经查，汞的原子量为200.59，钙的原子量为40.08。
3) by + n times
[6] The steel output has increased by two times.
钢产量已增加了一倍。
评析：即增加了（原数目-1）倍。
[7] The error probability of the equipment was reduced by 2.5 times through technical innovation.
通过技术革新，该设备的误差概率降低了3/5。
评析：reduced by 2.5 times，汉语中不说“降低到二点五”，这时应换算成整数分母，即降低到“五分之二”，或降低了“五分之三”。
[8] By using a new process the prime cost of the television set was reduced by 3.4 times.
采用一种新工艺使这种电视的主要成本降低了71%。
评析：算成整数分母，即“降低到5/17” 或“降低了12/17”，但这样仍不符合汉语习惯。在不要求绝对精确的情况下，可进一步换算成百分数，即“降低到29%”或“降低了71%”。
另外，由倍数换算成分数表示减少后的结果，译成“减少到几分之一”或“减少为几分之一”。例如，
reduce by 3 times 减少到1/3 或减少了2/3
reduce by 5 times 减少到1/5 或减少了4/5
reduce by 10 times 减少到1/10 或减少了9/10
4)“倍数+upon/over”结构表示“增加到n倍，增加了或超过了（n-1）倍”
[9] The industrial output in our factory this year is ten times over that of 1999.
今年我们工厂的产量比1999年增加10倍。（×）
今年我们工厂的产量是1999年的10倍。
[10] He is five times upon your age.
他是你年龄的5倍。
[11] The total output value of the city’s light industry has grown over three times as against last year.
这个城市的轻工业总产值比去年增长了两倍多。
[12] The number of the students in that school has been decreased more than 3 fold.
该校学生人数减少了2/3。（即减少到原来的1/3）
[13] The grain output in that county was two times over that of 1995.
那个县的粮食产量比1995年增加了一倍。
5) 增减意义的动词+倍数
应为“增加到原来的n倍”或 “增加了（n-1）倍”
[14] The cotton output in the county has increased four times.
该县棉花产量增加了3倍。
[15] The sales of TV set have risen 3.5 fold.
电视机销售量增加了2倍半。
[16] The weight of the bicycle has decreased 3 times.
这种自行车的重量减少了2/3。（即减少到1/3）
[17] The length of the rope has been shortened 5 fold.
绳子的长度缩短了4/5。（即缩短到1/5）
[18] If there were a bridge here, the distance would be shortened 4 times.
如果这里有座桥，距离将缩短3/4。
6)“表示增减意义的词+to+倍数”句型常译为“增（降）至n倍”
[19] The number of the students has increased to three times.
学生人数增加到3倍。
[20] The price of rice has reduced to two thirds.
大米的价格减到原价的2/3。
① Exceed (increase, decrease, reduce)+by a factor of +倍数
增加到n倍，减少到1/n倍
[21] The speed exceeded the average speed by a factor of 2.5.
该速度超过平均速度的1.5倍。
[22] The price of farm tools has decreased by a factor of 4.
农具降到原价的1/4。
[23] This equipment will reduce the error probability by a factor of 5.
这种设备使误差概率降低到原来的1/5。
② 表示“2倍”时，不能用two times，除了twice外，还可以用double， as …again as等
[24] He demanded double the usual fee.
他要了比平常多1倍的路费。
[25] A is as long again as B.
A的长度是B的2倍。
③ 表示“3倍”时，除可用three times外，还可用动词treble或triple等表示。
[26] The grains in the area have trebled this year.
今年这个地区的粮食增加了2倍。
[27] Output should triple by next year.
到明年产量应增至三倍。
④ 在表示“4倍”或“4倍以上”时，除用“基数词+times”外，还可用“基数词+fold”的合成词。
[28] We have produced four-fold as many electric fans as we did last year.
本年我们生产的电扇数量相当于去年的4倍。
[29] During that period its total output of industry increased (to) ten-fold.
在那个时期，工业总产值增加了9倍。
⑤ 在表示“不到1倍”时，还可用“分数+as …again as”表示。
[30] A is half as much again as B.
A比B多一半。
7) 倍数+the size (length, height) of …表示
[31] Shanghai is about 4 times the size of Changsha.
Shanghai is about 4 times as large as Changsha.
上海大约有长沙的4倍那么大。
[32] In this workshop the output of July was 3.5 times that of January.
In this workshop the output of July was 3.5 times as much as that of January.
这个车间7月份的产量是1月份的3.5倍。
补充：
倍数增加：
(一)
A is n times as great(long,much,…)as B.（1）
A is n times greater (longer,more,…)than B.（2）
A is n times the size (length,amount,…)of B.(3)
以上三句都应译为；A的大小（长度,数量…）是B的n倍
[或A比B大（长，多，……）n-1倍].
Eg. This book is three times as long as （three times longer than，three times the length of）that one.
这本书的篇幅是那本书的3倍（即长两倍）。
注：当相比的对象B很明显时，than（as，of）B常被省去。
(二)
increase to n times（4）
increase n times/n-fold（5）
increase by n times（6）
increase by a factor of n（7）
以上四式均应译为：增加到n倍（或：增加n-1倍）。
Eg. The production of integrated circuits has been increased to three times as compared with last year.
集成电路的产量比去年增加了两倍。
Eg. The output of chemical fertilizer has been raised five times as against l986．
化肥产量比1986年增加了4倍。
Eg. That can increase metabolic rates by two or three times.
那可使代谢率提高到原来的2倍或3倍（即提高1倍或2倍）。
Eg. The drain voltage has been increased by a factor of four.
漏电压增加了3借（即增加到原来的4倍）。
注：在这类句型中increase常被raise，grow，go/step up，multiply等词所替代。
(三)
There is a n-fold increase/growth…（8）
应译为：增加n-倍（或增至n倍）。
Eg. A record high increase in value of four times was reported.
据报道,价值破记录地增长了3倍。
(四)
double (增加1倍)，treble（增加2倍），quadruple（增加3倍）。(9)
Eg. The efficiency of the machines has been more than trebled or quadrupled．
这些机器的效率已提高了2倍或3倍多。
(五)
此外，英语中还有一种用again而不用倍数词来比较倍数的方法，如： A is as much (large，long，…)again as B.
A is twice as much (large，long，…)as B.（10）
应译为：A比B多（大，长，……）1倍。
A is half as much (large， 1ong，…)again as B.
A is one and a half times as much (large， 1ong，…)as B.（11）
应译为:A比B多（大，长……）一半（即A是B的一倍半）。
倍数减少：
(一)
A is n times as small (light，slow，…)as B.（12）
A is n times smaller (lighter， slower，…)than B.（13）
以上两句均应译为：A的大小(重量，速度，……)是B的1/n
[或A比B小(轻，慢，……) (n-1)/n]。
Eg. The hydrogen atom is nearly l6 times as light as the oxygen atom.
氢原子的重量约为氧原子的1/16（即比氧原子约轻15/16）。
Eg. This sort of membrane is twice thinner than ordinary paper.
这种薄膜比普通纸张要薄一半（即是普通纸厚度的1/2）。
注：当相比的对象B很明显时，than/as B常被省去。
(二)
decrease n times/n--fold（14）
decrease by n times（15）
decrease by a factor of n（16）
以上三式均译为：减少到1/n[或：减少(n-1)/n]。 decrease常被reduce， shorten， go/slow down等词替代。
Eg. Switching time of the new-type transistor is shortened 3 times. 新型晶体管的开关时间缩短了1/3（即缩短到2/3）。
Eg. When the voltage is stepped up by ten times，the strength of the current is stepped down by ten times.
电压升高9倍，电流强度便降低9/10（即90％）。
Eg. The equipment reduced the error probability by a factor of 5.
该设备误差概率降低了4/5。
(三)
There is a n-fold decrease/reduction…
应译为：减至1/n [或：减少(n一1)/n]。（17）
Eg. A rapid decrease by a factor of 7 was observed．
发现迅速减少到1/7。
Eg. The principal advantage of the products is a two-fold reduction in weight.
这些产品的主要优点是重量减轻了1/2。
从上面倍数增减句型及其译法中不难看出：与汉语不同的是，英语在表述或比较倍数时，无论使用什么句型(除了不含倍数词的again句型外)都包括基础倍数在内，因此都不是净增或净减n倍，而是净增或净减n-1倍。所以句型5、3表示的倍数增量=句型4；句型13表示的倍数比差＝句型12，且decrease(by)3 times应译为“减少2/3”，而不是“减少3/4”。