# ��ѧ���ż�����ʽӢ�����

17.2.1999/H. V�� aliaho

Pronunciation of mathematical expressions
The pronunciations of the most common mathematical expressions are given in the list below. In general, the shortest versions are preferred (unless greater precision is necessary). 1. Logic ? ? p?q p?q 2. Sets x��A x�� /A A?B A?B A��B A��B A\B A��B x belongs to A / x is an element (or a member) of A x does not belong to A / x is not an element (or a member) of A A is contained in B / A is a subset of B A contains B / B is a subset of A A cap B / A meet B / A intersection B A cup B / A join B / A union B A minus B / the di?erence between A and B A cross B / the cartesian product of A and B there exists for all p implies q / if p, then q p if and only if q /p is equivalent to q / p and q are equivalent

3. Real numbers x+1 x?1 x��1 xy (x ? y )(x + y ) x y = x=5 x=5 x plus one x minus one x plus or minus one xy / x multiplied by y x minus y , x plus y x over y the equals sign x equals 5 / x is equal to 5 x (is) not equal to 5 1

x��y x��y x>y x��y x<y x��y 0<x<1 0��x��1 |x| x2 x3 x4 xn x �� x �� 3 x �� 4 x �� n x x y n! x ? x ? x ? xi
n ?n

x is equivalent to (or identical with) y x is not equivalent to (or identical with) y x is greater than y x is greater than or equal to y x is less than y x is less than or equal to y zero is less than x is less than 1 zero is less than or equal to x is less than or equal to 1 mod x / modulus x x squared / x (raised) to the power 2 x cubed x to the fourth / x to the power four x to the nth / x to the power n x to the (power) minus n (square) root x / the square root of x cube root (of) x fourth root (of) x nth root (of) x x plus y all squared x over y all squared n factorial x hat x bar x tilde xi / x subscript i / x su?x i / x sub i

(x + y )2
2

ai
i=1

the sum from i equals one to n ai / the sum as i runs from 1 to n of the ai

4. Linear algebra x ? ? �� OA OA AT A?1 the norm (or modulus) of x OA / vector OA OA / the length of the segment OA A transpose / the transpose of A A inverse / the inverse of A 2

5. Functions f (x) f :S��T x��y f (x) f (x) f (x) f (4) (x) ?f ?x1 ?2f ?x2 1
�� 0 x��0 x��+0 x��?0

f x / f of x / the function f of x a function f from S to T x maps to y / x is sent (or mapped) to y f prime x / f dash x / the (?rst) derivative of f with respect to x f double�Cprime x / f double�Cdash x / the second derivative of f with respect to x f triple�Cprime x / f triple�Cdash x / the third derivative of f with respect to x f four x / the fourth derivative of f with respect to x the partial (derivative) of f with respect to x1 the second partial (derivative) of f with respect to x1 the integral from zero to in?nity

lim

the limit as x approaches zero the limit as x approaches zero from above the limit as x approaches zero from below log y to the base e / log to the base e of y / natural log (of) y log y to the base e / log to the base e of y / natural log (of) y

lim

lim

loge y ln y

Individual mathematicians often have their own way of pronouncing mathematical expressions and in many cases there is no generally accepted ��correct�� pronunciation. Distinctions made in writing are often not made explicit in speech; thus the sounds f x may ? ? �� be interpreted as any of: f x, f (x), fx , F X , F X , F X . The di?erence is usually made clear by the context; it is only when confusion may occur, or where he/she wishes to emphasise the point, that the mathematician will use the longer forms: f multiplied by x, the function f of x, f subscript x, line F X , the length of the segment F X , vector F X . Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes a di?erence in intonation or length of pauses) between pairs such as the following: x + (y + z ) and (x + y ) + z �� �� ax + b and ax + b an ? 1 and an?1 The primary reference has been David Hall with Tim Bowyer, Nucleus, English for Science and Technology, Mathematics, Longman 1980. Glen Anderson and Matti Vuorinen have given good comments and supplements. 3

Pronunciation of Mathematical Symbols
Symbols
+ �� x / �� = �� �� �� > < �� �� ? ? ? ? �� �O�O ? ?? ? ?
4

plus minus plus or minus multiplied by over; divided by divided equals approximately, similar equivalent to; identical not equal to greater than less than greater than or equal to less than or equal to not greater than not less than much greater than much less than perpendicular to parallel to

/'pl?s/ /'ma?n?s/ /'pl?s ?: 'ma?n?s/ /'m?lt?pla?d ba?/ /'??v?/ /d?'va?d?d/ /d?'va?d?d/ /'?:kw?lz/ /?'pr?ks?m?tl?/ /'s?m?l? t?/ /?k'w?v?l?nt t?/ /a?'dent?kl t?/ /'n?t 'i?kw?l t?/ /'gre?t? ??n/ /'les ??n/ /'gre?t? ??n ?r 'i?kw?l t?/ /'les ??n ?r' i?kw?l t?/ /'n?t 'gre?t? ??n/ /'n?t 'les ??n/ /'m?? 'gre?t? ??n/ /'m?? 'les ??n/ /p??p?n'd?kj?l? t?/ /'p?r?lel t?/

not equivalent to, not identical /'n?t ?k'w?v?l?nt t?/ /'n?t a?'dent?kl to t?/ not similar to squared cubed to the fourth; to the power four /'n?t 's?m?l? t?/ /'skwe?d/ /'kju:bd/ /t? ?? 'f??��/ /te ?? 'p��?? f??/

n

to the n; to the nth; to the power n root; square root cube root fourth root factorial percent infinity varies as; proportional to dot double dot is to, ratio of f; function f dash; derivative f double-dash; second derivative f triple-dash; f treble-dash; third derivative f four; fourth derivative partial derivative, delta integral sum with respect to log log to the base 2 of x therefore because gives, leads to, approaches per

/t? ?? en; t? d? en��; t? ?? p��??r en/ /ru:t/ /skwe? ru:t/ /kju:b ru:t/ /f??�� ru?t/ /f?k't??r??l/ /p?'sent/ /?n'f?n?t?/ /'v??r?z/ /pr?'p????n?l/ /d?t/ /d?bl d?t/ /re?????/ /ef/ /'f??k??n/ /d??/ /d?'r?v?t?v/ /'d?bl d??/ /'sek?nd d?'r?v?t?v/ /'tr?pl d??/ / trebl d??/ /��?:d d?'r?v?t?v/ /f??�� d?'r?v?t?v/ /pa???l d?'r?v?t?v/ /delt?/ /'?nt?gr?l/ /s?m/ /w?? 'r?spekt/ /l?g/ /l?g t? ?? be?s tu: ?v eks/ /'???f??/ /b?'k?z/ /g?vz/ /li:dz t?/ /?pr????z/ /p?:/

�� ? ? ! % �� �� �B �� : f(x) fx f'(x) f''x f'''(x) f(4) ? �� �� w.r.t. log log?x �� �� �� / ��

belongs to; a member of; an /b?'l??z/ /'memb?/ /'el?m?nt/

element of ? does not belong to; is not a /n?t b?'l??/ /n?t ? 'memb?/ /n?t ?n member of; is not an element 'el?m?nt/ of contained in; a proper subset /k?n'te?nd ?n/ /'pr?p? 's?bset/ of contained in; subset intersection union for all cos x; cosine x sine x tangent x cosec x shine x cosh x than x mod x; modulus x degrees Centigrade degrees Fahrenheit degrees Kelvin absolute zero /'s?bset/ /'?nt?sek??n/ /'ju?n??n/ /f? r?:l/ /k?z/ /sa?n/ /tan/ /'k??sek/ /'?a?n/ /'k??/ /��?n/ /m?d/ /'m?dj?l?s/ /d?'gri:z 'sent?gre?d/ /d?'gri:z 'f?r?nha?t/ /d?'gri:z 'kelv?n/ /abs?lu:t zi:r??/

? ? ? ? ? cos x sin x tan x cosec x sinh x cosh x tanh x |x| �� �H ��K 0��K, �C273.15 ��C mm cm

millimetre centimetre

/'m?l?mi?t?/ /'sent?mi?t?/ /'kju?b?k 'sent?mi?t?/ /'sent?mi?t? 'kju:bd/ /'mi?t?/ /k?'l?m?t?/ '/m?l?gr?m/

cc, cm?

cubic centimetre, centimetre cubed

m km mg

metre kilometre milligram

g kg AC DC

gram kilogram A.C. D.C.

/gr?m/ /'k?l?gr?m/ /e? si:/ /di: si:/

Examples
x+1 x -1 x��1 xy (x �� y)(x + y) x/y x��y x=5 x��y x��y x��y x>y x<y x��y x��y 0<x<1 0��x��1 x? x? x x x ? ?
4 n -n

x plus one x minus one x plus or minus one x y; x times y; x multiplied by y x minus y, x plus y x over y; x divided by y; x divided by y x equals 5; x is equal to 5 x is approximately equal to y x is equivalent to y; x is identical with y x is not equal to y x is greater than y x is less than y x is greater than or equal to y x is less than or equal to y zero is less than x is less than 1; x is greater than zero and less than 1 zero is less than or equal to x is less than or equal to 1; x is greater than or equal to zero and less than or equal to 1 x squared x cubed x to the fourth; x to the power four x to the n; x to the nth; x to the power n x to the minus n; x to the power of minus n root x; square root x; the square root of x the cube root of x the fourth root of x

��

the nth root of x (x + y)? (x/y)? n! x% �� x �� y ? ? f(x) fx f'(x) f''x f'''(x) f(4) ?v ?v ?�� ??v ?��? dv dv d�� d?v d��? �� x plus y all squared x over y all squared n factorial; factorial n x percent infinity x varies as y; x is (directly) proportional to y x dot x double dot f of x; the function of x f dash x; the (first) derivative of with respect to x f double-dash x; the second derivative of f with respect to x f triple-dash x; f treble-dash x; the third derivative of f with respect to x f four x; the fourth derivative of f with respect to x the partial derivative of v delta v by delta theta, the partial derivative of v with respect to �� delta two v by delta theta squared; the second partial derivative of v with respect to �� the derivative of v d v by d theta, the derivative of v with respect to theta d 2 v by d theta squared, the second derivative of v with respect to theta, integral integral from zero to infinity �� sum the sum from i equals 1 to n w.r.t. logey �� with respect to log to the base e of y; log y to the base e; natural log (of) y therefore

x �� 1/y x varies as one over y; x is indirectly proportional to y

�� �� ��x �� 0 lim
��x��0

because gives, approaches delta x approaches zero the limit as delta x approaches zero, the limit as delta x tends to zero the limit as delta x approaches zero, the limit as delta x tends to zero metres per second x belongs to A; x is a member of A; x is an element of A x does not belong to A; x is not a member of A; x is not an element of A A is contained in B; A is a proper subset of B A is contained in B; A is a subset of B A intersection B A union B cos x; cosine x sine x tangent x, tan x cosec x shine x cosh x than x mod x; modulus x eighteen degrees Centigrade seventy degrees Fahrenheit

Lt
��x��0

m/sec x �� A x? A A? B A ? B A?B A?B cos x sin x tan x cosec x sinh x cosh x tanh x |x| 18 �� 70 �H

Greek alphabet
�� �� alpha �� �� beta �� �� delta /'?lf?/ /'bi:t?/ /'delt?/

�� �� gamma /'g?m?/ �� �� epsilon /'epsil?n/ �� �� zeta /'zi?t?/

�� �� eta �� �� theta �� �� iota

/'i?t?/ /'��i?t?/ /a?'??t?/ /'k?p?/ /'l?md?/ /'mju?/ /'nju?/ /'ksa?/ /'pa?/ /'r??/ /'s?gm?/ /'t��?/ /'fa?/ /'ka?/ /'psa?/

�� �� kappa �� �� lamda �� �� mu �� �� nu �� �� xi �� �� pi �� ��? rho �� �� sigma �� �� tau

�� �� omicron /'??m?kr?n

�� �� upsilon /'j?ps?l?n/ �� �� phi �� �� chi �� �� psi

? �� omega /'??m?g?

Fractions
? a half ? a quarter /? 'h��:f/ /? 'kw??t?/

? three quarters /��ri? 'kw??t?z/ ? a third ? two thirds ? a fifth ? two fifths ? three fifths /? '��?:d/ /tu: '��?:dz/ /? 'f?f��/ /tu: 'f?f��s/ /��ri? 'f?f��s/

? four fifths ? a sixth ? five sixths ? an eighth

/f?? 'f?f��s/ /? 's?ks��/ /fa?v 's?ks��s/ /?n 'e?t��/

? three eighths /��ri? 'e?t��s/ ? five eighths /fa?v 'e?t��s/

? seven eighths /sev?n 'e?t��s/

Decimal Fractions
0.1 0.01 0.0001 1.1 1.2 1.23 1.0123 10.01 21.57 2.6666666666.... 2.612361236123... 2.5 million nought point one nought point oh one one point one one point two one point two three ten point oh one twenty-one point five seven two point six recurring /n?:t p??nt w?n/ /n?:t p??nt ?? w?n/ /w?n p??nt w?n/ /w?n p??nt tu:/ /w?n p??nt tu: ��ri:/ /ten p??nt ?? w?n/ /'twent? w?n p??nt fa?v 'sev?n/ /tu: p??nt s?ks r?'k?:r??/

nought point oh oh oh one /ten p??nt ?? ?? ?? w?n/

one point oh one two three /w?n p??nt ?? w?n tu: ��ri:/

two point six one two three /tu: p??nt s?ks w?n tu: ��ri: recurring r?'k?:r??/ two point five million /tu: p??nt fa?v 'm?lj?n/

SI Units: Prefixes
10-24 yocto y /j'?kt??/ 10-21 zepto z /'zept??/ 10-18 atto 10 10 10
-15 -12 -9

a /'at??/ p /'pi:k??/

femto f /'femt??/ pico nano n /'nan??/

10-6 micro ? /'ma?kr??/ 10-3 milli 10-1 deci 103 kilo m /'m?l?/ d /'des?/ k /'k?l??/ 10-2 centi c /'sent?/

106 mega M /'meg?/ 109 giga G /'gi:g?/ 1012 tera 1018 exa T /'ter?/ E /'eks?/ 1015 peta P /'pet?/ 1021 zeta Z /'zet?/ 1024 yota Y /'j?t?/

Cardinal Numbers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen /w?n/ /tu:/ /��ri:/ /f??/ /fa?v/ /s?ks/ /'sev?n/ /e?t/ /na?n/ /ten/ /?'lev?n/ /twelv/ /��?:'ti:n/ /f??'ti:n/ /f?f'ti:n/ /s?kst'i:n/ /seven'ti:n/ /e?'ti:n/

19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 70 80 90 100 101 102 110 120 200 300 400 500 600 700 800 900 1 000

nineteen twenty twenty-one twenty-two twenty-three twenty-four twenty-five twenty-six twenty-seven twenty-eight twenty-nine thirty forty fifty sixty seventy eighty ninety a hundred; one hundred a hundred and one a hundred and two a hundred and ten a hundred and twenty two hundred three hundred four hundred five hundred six hundred seven hundred eight hundred nine hundred a thousand, one thousand

/na?n'ti:n/ /'twent?/ /twent?'w?n/ /twent?'tu:/ /twent?'��ri:/ /twent?'f??/ /twent?'fa?v/ /twent?'s?ks/ /twent?'sev?n/ /twent?'e?t/ /twent?'na?n/ /'��?:t?/ /'f??t?/ /'f?ft?/ /'s?kst?/ /'sevent?/ /'e?t?/ /'na?nt?/ /? 'h?ndr?d/ /w?n 'h?ndr?d/ /? 'h?ndr?d ?n w?n/ /? 'h?ndr?d ?n tu:/ /? 'h?ndr?d ?n ten/ /? 'h?ndr?d ?n 'twent?/ /tu: 'h?ndr?d/ /��ri: 'h?ndr?d/ /f?? 'h?ndr?d/ /fa?v 'h?ndr?d/ /s?ks 'h?ndr?d/ /'sev?n 'h?ndr?d/ /e?t 'h?ndr?d/ /na?n 'h?ndr?d/ /? ��'��?z?nd/ /w?n '�Ȩ�?z?nd/

1 001 1 010 1 020 1 100 1 101 1 110 9 999 10 000 15 356 100 000 100 000 000

a thousand and one a thousand and ten a thousand and twenty one thousand, one hunded one thousand, one hundred and one one thousand, one hundred and ten nine thousand, nine hundred and ninety-nine ten thousand fifteen thousand, three hundred and fifty six a hundred thousand

/? '�Ȩ�?z?nd ?n w?n/ /? '�Ȩ�?z?nd ?n ten/ /? '�Ȩ�?z?nd ?n 'twent?/ /w?n '�Ȩ�?z?nd w?n 'h?ndr?d/ /w?n '�Ȩ�?z?nd w?n 'h?ndr?d ?n w?n/ /w?n '�Ȩ�?z?nd w?n 'h?ndr?d ?n ten/ /na?n '�Ȩ�?z?nd na?n 'h?ndr?d ?n 'na?nt? 'na?n/ /ten '�Ȩ�?z?nd/ /'f?fti:n '�Ȩ�?z?nd ��ri: 'h?ndr?d ?n 'f?ft? s?ks/ /? 'h?ndr?d '�Ȩ�?z?nd/ /? 'm?lj?n/ /? 'h?ndr?d 'm?lj?n/ /? 'b?lj?n/ /? 'h?ndr?d 'b?lj?n/ /? 'tr?lj?n/

1 000 000 a million a hundred million

1 000 000 a billion 000 100 000 000 000 a hundred billion

1 000 000 a trillion 000

Ordinal Numbers
1st 3rd 4th 5th 6th 7th 8th 9th first third fourth fifth sixth seventh eighth ninth /f?:st/ /'sek?nd/ /��?:d/ /f?:��/ /f?f��/ /s?ks��/ /'sev?n��/ /e?t��/ /na?n��/ /ten��/

2nd second

10th tenth

11th eleventh 12th twelfth 13th thirteenth 14th fourtheenth 15th fidteenth 16th sixteenth 17th seventeenth 18th eighteenth 19th nineteenth 20th twentieth 21st twenty-first 23rd twenty-third 24th twenty-fourth 25th twenty-fifth 26th twenty-sixth 28th twenty-eighth 29th twenty-ninth 30th thirtieth 31st thirty-first

/?'lev?n��/ /'twelf��/ /��?:'ti:n��/ /f??'ti:n��/ /f?f'ti:n��/ /s?ks'ti:n��/ /seven'ti:n��/ /e?'ti:n��/ /na?n'ti:n��/ /'twent??��/ /twent?'f?:st/ /twent?'��?:d/ /twent?'f?:��/ /twent?'f?f��/ /twent?'s?ks��/ /twent?'e?t��/ /twent?'na?n��/ /'��??t??��/ /��??t?'f?:st/

22nd twenty-second /twent?'sek?nd/

27th twenty-seventh /twent?'sev?n��/

��ѧ���ŵ�Ӣ�����
1.Cardinals and Ordinals ����������

(1)100 ���ڵ����� ���� ���� Roman Arabic Numerals Numerals �������� ���������� ���� ���� ���� I 1 one 1st the first II 2 two 2nd the second III 3 three 3rd the third IV 4 four 4th the fourth V 5 five 5th the fifth VI 6 six 6th the sixth VII 7 seven 7th the seventh VIII 8 eight 8th the eighth IX 9 nine 9th the ninth X 10 ten 10th the tenth XI 11 eleven 11th the eleventh XII 12 twelve 12th the twelfth XIII 13 thirteen 13th the thirteenth XIV 14 fourteen 14th the fourteenth

XV 15 fifteen 15th the fifteenth XVI 16 sixteen 16th the sixteenth XVII 17 seventeen 17th the seventeenth XVIII 18 eighteen 18th the eighteenth XIX 19 nineteen 19th the nineteenth XX 20 twenty 20th the twentieth XXI 21 twenty-one 21st the twenty-first XXV 25 twenty-five 25th the twenty-fifth XXX 30 thirty 30th the thirtieth XL 40 forty 40th the fortieth L 50 fifty 50th the fiftieth LX 60 sixty 60th the sixtieth LXX 70 seventy 70th the seventieth LXXX 80 eighty 80th the eightieth XC 90 ninety 90th the ninetieth IC 99 ninety-nine 99th the ninety-ninth C 100 one hundred 100th the hundredth CII 102 a hundred 102nd the (one) hundred and two and second 246 two hundred and forty-six 751 seven hundred and fifty-one

(2)1000 ���ϵ����� 1,000 = one thousand һǧ 10,000 = ten thousand һ�� 100,000 = one hundred thousand ʮ�� 1,000,000 = one million һ���� 10,000,000 = ten million һǧ�� 100,000,000=one hundred million һ��

(3)ʮ�����ϵĴ�����Ӣ���в�ͬ�Ķ����� Ӣ�� ���� ʮ�� one thousand million = one billion ���� ten thousand million = ten billion ǧ�� one hundred thousand million = one hundred billion ���� one billion = one trillion

2.Fractions ����

ͨ�������Ӷ�Ϊ����������ĸ��Ϊ������ 1/2 = a (or one) half 1/3 = a (or one) third 1/4 = a quarter or one fouth 1/5 = a (or one) fifth

2/3 = two thirds 9/10 = nine tenths 53/4 = five and three quarters 15/64= fifteen over (or by) sixty-four 15% = fifteen per cent 4�� = four per mill

3.Decimals С��

0.4 = zero (or

nought ) point four

.01 = point (or decimal) nought one 12.34 = twelve point three four 567.809 = five hundred and sixty-seven point eight nought nine 30.45 = thirty point four five, five recurring 0.3% = decimal three percent

4.Mathematic Forms ��ѧʽ

(1) Addition �ӷ� 1+2=3 One and two are three. 2+3=5 Two plus three equals five. 4+0=4 Four and nought is equal to four.

45+70+152=267 45,70 and 152 added are (or make) 267 the sum (or total) is 267. ����ʱ�Ķ����� Three and seven are ten; I write(or I write down,or I put down)a nought and carry one. Four and one that I carry are five, and eight make thirteen,and three sixteen; I write down six and carry one. One and one (that I carry) are two; I put down two.- The sum (or total, or the result of the addition) is two hundred and sixty. 37,80 and 143 added together, and(or make) 260.

(2)Subtraction ���� 9-4=5 Nine minus four equals (or is equal to) five. 15-7=8 Seven from fifteen leaves eight. 23,654-8,175=15,479 8,175 (take or subtracted) from 23,654 leaves 15,479. The difference (or The remainder) is 15,479. Nine from five won`t go. �� �� ʱ �� �� �� �� Nought from nought (leaves) nought. One from one leaves nought (or nothing). Two from three (leaves) one. I can`t take (or subtract) five from four; I

must borrow ten; five from fourteen leaves nine.- The difference (or The remainder) is nine thousand one hundred. 5210 (take or substracted) from 14,310 leaves 9,100.

(3)Multiplication �˷� 1��0=0 One multiplied by nought equals nought. 1��1=1 Once one is one. 2��1=2 Twice one is two. 3��5=15 Three times five is fifteen 6��0=0 Multiply six by nothing, and the result is nothing. ����ʱ�Ķ���: Five times nine (or Nine multiplied by five) are forty-five; I put down five and carry four. Five times seven are thirty-five and four (that I carry) are thirty-nine; I write down nine and carry three. Five times six make thirty and three (that I carry) thirty-three; I put down thirty-three. Eight times nine (or Eight nine) are seven two; I write two and carry seven. Eight sevens make fifty-six and seven are sixty-three. I put down three and carry six. Eight sixes make forty-eight

and six fifty-four; I write down fifty-four. I now add the partial results (or products) Five. Two and nine are eleven. Three and three are six and one are seven. Four and three make seven. Five.

(4)Division ���� 9��3=3 Nine divided by three maks (or is equal to) three. 20��5=4 Five into twenty goes four times. 4567��23=198 �� 13 23 into 4567 goes 198 times, and 13 remainder. The quctient is 198, and 13 remainder. ����ʱ�Ķ��� : Fifteen into thirteen won`t go ; fifteen into one hundred and thirty-eight goes nine times; nine times fifteen are one hundred and threty-five; one hundred and thirty-five from one hundred and thirty-eight leaves three; I bring down seven; fifteen into thirty-seven goes twice; twice fifteen are thirty; thirty from thirty-seven leaves seven. The (exact) quotient is ninety-two, and seven remainder; 15 into 1387 goes 92 times, and 7 remainder.

5.Time ʱ��

(1)Hours �ӵ� 2h.5'8" = two hours five minutes eight seconds 2 Сʱ 5 �� 8 �� 6.18 = six eighteen 6 ʱ 18 �� 8.30 a.m.= eight thirty a.m.['ei 'em] ���� 8 ʱ 30 �� the 6.05 p.m.train = the six (nought) five p.m.['pi:'em] train ���� 6 ʱ�� 5 ���г� �ֶ�ʮ��Сʱ����Ƶ�д���Ͷ������£� 0900 = 0 nine hunderd (����)9 ʱ 0910 = 0 nine ten (����)9 ʱ 10 �� 1300 = thirteen hundred 13 ʱ(���� 1 ʱ) 1525 = fifteen twenty-five 15 ʱ 25 ��(���� 3 ʱ 25 ��) 2000 = twenty hundred 20 ʱ(���� 8 ʱ) at 5 o'c =at five o'clock �����

(2)Date ���� Oct.1 =October first 10 �� 1 �� Oct.1st = October the first 10 �� 1 �� Ist Oct. 1949 = teh first of October, nineteen forty-nine 1949 �� 10 �� 1 �� 3/5 = [Ӣ]May (the) third 5 �� 3 �գ�[��]March fifth 3 �� 5 �� [��ע]��ϵ����ǰ�ô��� on.

(3)Year ���

684 B.C. =Six eighty-four B.C. ['bi:'si:] ��Ԫǰ 684 �� 1960 = nineteen sixty; nineteen hundred and sixty 19- nineteen something 1950's nineteen fifties ��ʮ������ʮ��� [��ע]��ϵ��ݵ�ǰ�ô��� in.

6.Numbers ����

(1)Telephones Numbers �绰���� 1023 = one O two three; ten twenty-three 1227 = one double two (or two two) seven 0386 = O three eight six 0096 = double O(or O O )nine six 7000 = seven O double O = seven thousand No.26= Number 26 �� 26 �� Room 201 = Room two O one �� 201 ���� 10 Changan Street = Ten Changan Street ������ 10 ��

(2)Writings �鼮��Ʒ Vol.I = Volume one (or the first volume) ��һ Chap.II= Chapter two (or the second chapter) �� 2 ��

Page 3 = page Three (or the third page) �� 3 ҳ See pp.5-10 = See Pages five to ten ���� 5-10 ҳ Act V = Act five (or the fifth act) �� 5 Ļ Hamlet III 1:56 = Hamlet Act Three, Secene One.Line fifty-six ����ķ�� �ء��� 3 Ļ��һ���� 56 �� Matt.7:12 = Matthew, Chapter Seven, Verse Twelve �����ɸ��������� �µ� 12 �� Beethoven Op.49 = Beethoven Opus forty-nine �������Ʒ�� 49 �� 4to = quarto �ı��� 8vo = octavo �˱���

(3)Other ���� World War I = World War One ��һ�������ս World War II = World War Two �ڶ��������ս Charles I= Charles the First ����һ�� Henry V = Henry the Fifth �������� Mr.- = Mr. Dash; Mr. So-and-so ĳĳ���� Mr.B - = Mr. B -Esq.,of -= the town of Blank Esquire of Blank University ĳ��ѧĳĳ ���� the town of = the town of Blank ĳĳ�� The result of the game was 3-0 ��������������㡣

7.Money ����

(1)British currency Ӣ�� 6d. = six pence ����ʿ 1/2d. = a halfpenny ���ʿ 11/2d. = a peney halfpenny or three halfpeny or three halfpence һ��ʿ�� 1/4d. = a farthing һ��ͭԪ 33/4d.= three pence three farghings ����ʿ��ͭԪ 1s.6d.(or 1/6) = one (shilling) and six (pence) һ��������ʿ ��1.18 = (or��1.18s.)= one pound eighteen (shillings) һ��ʮ������ ��1.3s.6d. = one pound, three shillings (and) sixpence 4/51/2(or4s.51/2d.) = four (shillings) and five pence halfpenny

(2)U.S. currency 1.20 dollar (and) twenty (cents) ����һԪ���� 4.25 = four dollars twenty-five cents ������Ԫ�������

(3)Soviet currency ǰ������ 6 Rb. 15 = six roubles fifteen kopecks ��¬��ʮ����

(4) German currency �±�

1 m. 60 = one mark sixty pfennig -������ʮ����

(5)French currency ������ 1 fr.30 = one franc. thirty (centimes) -������ʮ���� 0 fr.15 = fifteen centimes ʮ������

(6) Chinese People's Currency ����� 1.50 = one yuan and a half һԪ��� JMP 10.35 = JMP ten yuan thirty-five (fen) �����ʮԪ������� ��ע��yuan ������û�б仯�� Ҳ����Ϊ�ձ���λ�ҡ�Բ���ķ��š�

8. Weight and Measures ������

(1) length, area, and volume ���ȡ�������ݻ� 3 in = three inches ��Ӣ�� 15 ft.5 in = fifteen foot five (inches) ʮ��Ӣ����Ӣ�� [��ע] ������ inches ʡ��ʱ, ft.���� foot;��� inches Ҳ�������ft �� �Զ��� fett. 18'6 5/1"= eighteen foot six and a fifth (inches) 10��8feet= ten by eight feet ʮӢ�߳�����Ӣ�߿� 5"��4��31/2 = five inches by four by three and a half ����Ӣ�磬 ����Ӣ

�磬����Ӣ��� [��ע] ���϶����У��˺š���ʾ������ݻ���

(2)Weight ���� 12 dr. 23 gr.= Twelve drams twenty-three grains ʮ��������ʮ��� 10 oz. 4 dr. = Ten ounces four drams ʮ��˾����

(3)Capacity ���� 3 gi. = three gills ������ 1 qt. 1 pt = one quart one pint һ����һƷ�� [��ע] qt.,pt. �ĸ����� qts.,pts.,Ҳ���Բ��� s. 20 gal. 5 qt. =Twenty gallons five quarts ��ʮ��������� 5 bu. 3 pk. = Five bushels three pecks ����ʽ�������

���ŵ�Ӣ�Ķ���

�� period ��� �� is approximately equal to Լ���ں� �� comma ���� �� is less than С�ں� �� colon ð�� �� is more than ���ں�

�� semicolon �ֺ� �� is not less than ��С�ں� �� exclamation ��̾�� �� is not more than �����ں� �� question mark �ʺ� �� is less than or equal to С�ڻ���ں� �� hyphen ���ַ� �� is more than or equal to ���ڻ���ں� ' apostrophe ʡ�Ժ� �����и���� �� per cent �ٷ�֮�� - dash ���ۺ� �� per mill ǧ��֮�� ' ' single quotation marks ������ �� infinity ���޴�� double quotation marks ˫���� �� varies as �롭�ɱ��� ( ) parentheses Բ���� �� (square) root ƽ���� [ ] square brackets ������ �� since; because ��Ϊ �� �� French quotes ��������;������

�� hence ���� ... ellipsis ʡ�Ժ� �� equals, as (proportion) ���ڣ��ɱ��� �� tandem colon ˫��� �� angle �� ditto ˫��� �� semicircle ��Բ �� parallel ˫�ߺ� �� circle Բ �� virgule б�ߺ� �� circumference Բ�� �� ampersand = and �� pi Բ���� �� swung dash ���ֺ� �� triangle ������ �� section; division �ֽں� �� perpendicular to ��ֱ�� �� arrow ���ţ��μ��� �� union of �����ϼ� �� plus �Ӻţ����� �� intersection of ����ͨ�� �� minus ���ţ�����

�� the integral of ���Ļ��� �� plus or minus ������ ( �� sigma) summation of �ܺ� �� is multiplied by �˺� �� degree �� �� is divided by ���� �� minute �� �� is equal to ���ں� �� second �� �� is not equal to �����ں� �� number ���� �� is equivalent to ȫ���ں� �� Celsius system ���϶� �� is equal to or approximately equal to ���ڻ�Լ���ں� �� at ����

R�� R��

R prime R double prime, R second prime

R1 R sub one 100�� C one hundred degrees Centigrade + plus; positive - minus; negative

& acute; multiplied by; times & cedil; divided by �� plus or minus = is equal to; equals & ordm; is identically equal to & raquo; is approximately equal to ( ) round brackets; parentheses [ ] square brackets { } braces a����b a is much greater than b a&sup3; b a is greater than or equal to b a&micro; b a varies directly as b lognX logX to the base n the cubic root of x the nth root of x x2 x square, x squared, the square of x Xn X to n factors; the nth power of x; x to the power n x -8 x to the minus eighth power &iuml; x&iuml; the absolute value of x the mean value of X the sum of the terms indicated; summation of D x or d x the increment of x

dx differential x dy/dx the first derivative of y with respect to x �� integral & yen; infinity 1/2 a half; one half 2/3 two thirds 5/123 five over a hundred and twenty-three eight and three over fourths; eight and three quarters 0.01 O point O one; zero point zero one; nought point nought one 6 % 6 percent 3�� 3 per mille 2 : 3 the ratio of two to three r=xd r equals x multiplied by d 5&acute; 2=10 five times two equals ten x3/8=y2 x raised to the third power divided by eight equals y squared (a+b-c&acute; d)/e=f a plus b minus c multiplied by d, all divided by e equals f y = (Wt-W)/x y equals W sub t minus W over x