Technical notes‎ > ‎

Mathematical and scientific symbols

posted Mar 4, 2017, 6:26 AM by Le Tuan Anh   [ updated Mar 4, 2017, 6:26 AM ]

Source: http://www.uefap.com/speaking/symbols/symbols.htm

Common pronunciations (in British English - Gimson,1981) of mathematical and scientific symbols are given in the list below.

(all the pages in this section need a unicode font installed - e.g. Arial Unicode MS, Doulos SIL Unicode, Lucida Sans Unicode - see: The International Phonetic Alphabet in Unicode).

Symbols

+ plus /'plʌs/
- minus /'maɪnəs/
± plus or minus /'plʌs  ɔ:  'maɪnəs/
x multiplied by /'mʌltɪplaɪd baɪ/
/ over; divided by /'əʊvə/ /dɪ'vaɪdəd/
÷ divided /dɪ'vaɪdəd/
= equals /'ɪ:kwəlz/
approximately, similar /ə'prɒksɪmətlɪ/ /'sɪmɪlə tʊ/
equivalent to; identical /ɪk'wɪvələnt tʊ/ /aɪ'dentɪkl tʊ/
≠  not equal to /'nɒt 'iːkwəl tʊ/
greater than /'greɪtə ðən/
less than /'les ðən/
≥  greater than or equal to /'greɪtə ðən ər 'iːkwəl tʊ/
≤  less than or equal to /'les ðən ər' iːkwəl tʊ/
not greater than /'nɒt 'greɪtə ðən/
not less than /'nɒt 'les ðən/
much greater than /'mʌʧ 'greɪtə ðən/
much less than /'mʌʧ 'les ðən/
perpendicular to /pɜːpən'dɪkjʊlə tʊ/
∣∣ parallel to /'pærəlel tʊ/
not equivalent to, not identical to /'nɒt ɪk'wɪvələnt tʊ/ /'nɒt aɪ'dentɪkl tʊ/
≄≉ not similar to /'nɒt 'sɪmɪlə tʊ/
² squared /'skweəd/
³ cubed /'kju:bd/
4 to the fourth;  to the power four /tə ðə 'fɔːθ/ /te ðə 'pɑʊə fɔː/
n  to the n; to the nth; to the power n /tə ðɪ en; tə dɪ enθ; tə ðə pɑʊər en/
root; square root /ru:t/ /skweə ru:t/
cube root /kju:b ru:t/
fourth root  /fɔːθ ruːt/
! factorial /fæk'tɔːrɪəl/
% percent /pə'sent/
infinity /ɪn'fɪnətɪ/
varies as; proportional to /'vɛərɪz/  /prə'pɔːʃənəl/
˙ dot /dɒt/
¨ double dot /dʌbl dɒt/
: is to, ratio of /reɪʃɪəʊ/
f(x) fx f; function /ef/ /'fʌŋkʃən/
f'(x) f dash; derivative  /dæʃ/ /dɪ'rɪvətɪv/
f''x f double-dash; second derivative /'dʌbl dæʃ/ /'sekənd dɪ'rɪvətɪv/
f'''(x) f triple-dash; f treble-dash; third derivative /'trɪpl dæʃ/ / trebl dæʃ/ /θɜ:d dɪ'rɪvətɪv/
f(4) f four; fourth derivative  /fɔːθ dɪ'rɪvətɪv/
partial derivative, delta /paːʃəl dɪ'rɪvətɪv/ /deltə/
integral /'ɪntɪgrəl/
sum /sʌm/
w.r.t. with respect to /wɪð 'rɪspekt/
log log  /lɒg/
logx log to the base 2 of x /lɒg tə ðə beɪs tu: əv eks/
therefore /'ðɛəfɔː/
because /bɪ'kɒz/
gives, leads to, approaches /gɪvz/ /li:dz tʊ/ /əprəʊʧəz/
/ per /pɜ:/
belongs to; a member of;  an element of /bɪ'lɒŋz/ /'membə/ /'elɪmənt/
does not belong to; is not a member of; is not an element of /nɒt bɪ'lɒŋ/ /nɒt ə 'membə/ /nɒt ən 'elɪmənt/
contained in;  a proper subset of /kən'teɪnd ɪn/ /'prɒpə 'sʌbset/
contained in; subset  /'sʌbset/
intersection /'ɪntəsekʃən/
union /'juːnɪən/
for all /fə rɔ:l/
cos x cos x; cosine x /kɒz/
sin x sine x /saɪn/
tan x tangent x /tan/
cosec x cosec x /'kəʊsek/
sinh x shine x /'ʃaɪn/
cosh x cosh x /'kɒʃ/
tanh x than x /θæn/
|x| mod x; modulus x /mɒd/ /'mɒdjʊləs/
degrees Centigrade /dɪ'gri:z 'sentɪgreɪd/
degrees Fahrenheit /dɪ'gri:z 'færənhaɪt/
°K degrees Kelvin /dɪ'gri:z 'kelvɪn/
0°K, –273.15 °C absolute zero /absəlu:t zi:rəʊ/
mm millimetre /'mɪlɪmiːtə/
cm centimetre /'sentɪmiːtə/
cc, cm³ cubic centimetre, centimetre cubed /'kjuːbɪk 'sentɪmiːtə/ /'sentɪmiːtə 'kju:bd/
m metre /'miːtə/
km kilometre /kɪ'lɒmɪtə/
mg milligram /'mɪlɪgræm/
g gram /græm/
kg kilogram /'kɪləgræm/
AC A.C. /eɪ si:/
DC D.C. /di: si:/

Examples

x + 1 x plus one
x -1 x minus one
x ± 1 x plus or minus one
xy x y;  x times y; x multiplied by y
(x — y)(x + y)  x minus y, x plus y
x/y x over y;  x divided by y;
x ÷ y x divided by y
x = 5 x equals 5;  x is equal to 5
x ≈ y x is approximately equal to y
x ≡ y x is equivalent to y;  x is identical with y
x ≠ y x is not equal to y
x > y  x is greater than y
x < y  x is less than y
x ≥ y x is greater than or equal to y
x ≤ y x is less than or equal to y
0 < x < 1 zero is less than x is less than 1; x is greater than zero and less than 1
0 ≤ x ≤ 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
x4 x to the fourth;  x to the power four
xn x to the n; x to the nth;  x to the power n
x-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)² x plus y all squared
(x/y)² x over y all squared
n! n factorial; factorial n
x% x percent
infinity
x ∝ y x varies as y; x is (directly) proportional to y
x ∝ 1/y x varies as one over y; x is indirectly proportional to y
x dot
x double dot
f(x) fx f of x; the function of x
f'(x) f dash x; the (first) derivative of with respect to x
f''x f double-dash x; the second derivative of f with respect to x
f'''(x) f triple-dash x; f treble-dash x; the third derivative of f with respect to x
f(4) f four x; the fourth derivative of f with respect to x
∂v the partial derivative of v
∂v
∂θ
delta v by delta theta, the partial derivative of v with respect to θ
²v
∂θ²
delta two v by delta theta squared; the second partial derivative of v with respect to θ
dv the derivative of v
dv
d v by d theta, the derivative of v with respect to theta
d²v
²
d 2 v by d theta squared, the second derivative of v with respect to theta, 
integral
integral integral from zero to infinity
sum
the sum from i equals 1 to n
w.r.t. with respect to
logey log to the base e of y; log y to the base e; natural log (of) y
therefore
because
gives, approaches
Δx → 0 delta x approaches zero
lim
Δx→0
the limit as delta x approaches zero, the limit as delta x tends to zero
Lt
Δx→0
the limit as delta x approaches zero, the limit as delta x tends to zero
m/sec metres per second
x ∈ A x belongs to A; x is a member of A; x is an element of A
x∉ A x does not belong to A; x is not  a member of A; x is not an element of A
A⊂ B A is contained in B; A is a proper subset of B
A ⊆ B A is contained in B; A is a subset of B
A ⋂ B A intersection B
A ⋃ B A union B
cos x cos x; cosine x
sin x sine x
tan x tangent x, tan x
cosec x cosec x
sinh x shine x
cosh x cosh x
tanh x than x
|x| mod x; modulus x
18 ℃ eighteen degrees Centigrade
70 ℉ seventy degrees Fahrenheit

Greek alphabet

Α α alpha /'ælfə/
Β β beta /'bi:tə/
Γ γ gamma /'gæmə/
Δ δ delta /'deltə/
Ε ε epsilon /'epsilən/
Ζ ζ zeta /'ziːtə/
Η η eta /'iːtə/
Θ θ theta /'θiːtə/
Ι ι iota /aɪ'əʊtə/
Κ κ kappa /'kæpə/
Λ λ lamda /'læmdə/
Μ μ mu /'mjuː/
Ν ν nu /'njuː/
Ξ ξ xi /'ksaɪ/
Ο ο omicron /'əʊmɪkrən/
Π π pi /'paɪ/
Ρ ρς rho /'rəʊ/
Σ σ sigma /'sɪgmə/
Τ τ tau /'tɑʊ/
Υ υ upsilon /'jʊpsɪlən/
Φ φ phi /'faɪ/
Χ χ chi /'kaɪ/
Ψ ψ psi /'psaɪ/
Ω ω omega /'əʊmɪgə/

Roman alphabet

A a /'eɪ/
B b /'biː/
C c /'siː/
D d /'diː/
E e /'iː/
F f /'ef/
G g /'ʤiː/
H h /'eɪʧ/
I i /'aɪ/
J j /'ʤeɪ/
K k /'keɪ/
L l /'el/
M m /'em/
N n /'en/
O o /'əʊ/
P p /'piː/
Q q /'kjuː/
R r /'ɑː/
S s /'es/
T t /'ti:/
U u /'ju:/
V v /'vi:/
W w /'dʌbljuː/
X x /'eks/
Y y /'waɪ/
Z z /'zed/

Fractions

½ a half /ə 'hɑ:f/
¼ a quarter /ə 'kwɔːtə/
¾ three quarters /θriː 'kwɔːtəz/
a third /ə 'θɜ:d/
two thirds /tu: 'θɜ:dz/
a fifth /ə 'fɪfθ/
two fifths /tu: 'fɪfθs/
three fifths /θriː 'fɪfθs/
four fifths /fɔː 'fɪfθs/
a sixth /ə 'sɪksθ/
five sixths /faɪv 'sɪksθs/
an eighth /ən 'eɪtθ/
three eighths /θriː 'eɪtθs/
five eighths /faɪv 'eɪtθs/
seven eighths /sevən 'eɪtθs/

Decimal Fractions

0.1 nought point one /nɔ:t pɔɪnt wʌn/
0.01 nought point oh one /nɔ:t pɔɪnt əʊ wʌn/
0.0001 nought point oh oh oh one /ten pɔɪnt əʊ əʊ əʊ wʌn/
1.1 one point one /wʌn pɔɪnt wʌn/
1.2 one point two /wʌn pɔɪnt tu:/
1.23 one point two three /wʌn pɔɪnt tu: θri:/
1.0123 one point oh one two three /wʌn pɔɪnt əʊ wʌn tu: θri:/
10.01 ten point oh one /ten pɔɪnt əʊ wʌn/
21.57 twenty-one point five seven /'twentɪ wʌn pɔɪnt  faɪv 'sevən/
2.6666666666.... two point six recurring /tu: pɔɪnt  sɪks rɪ'kɜ:rɪŋ/
2.612361236123... two point six one two three recurring /tu: pɔɪnt  sɪks wʌn tu: θri: rɪ'kɜ:rɪŋ/
2.5 million two point five million /tu: pɔɪnt  faɪv 'mɪljən/

SI Units: Prefixes

10-24 yocto y /'jɒktəʊ/
10-21 zepto z /'zeptəʊ/
10-18 atto a /'atəʊ/
10-15 femto f /'femtəʊ/
10-12 pico p /'pi:kəʊ/
10-9 nano n /'nanəʊ/
10-6 micro µ /'maɪkrəʊ/
10-3 milli m /'mɪlɪ/
10-2 centi c /'sentɪ/
10-1 deci d /'desɪ/
103 kilo k /'kɪləʊ/
106 mega M /'megə/
109 giga G /'gɪgə/
1012 tera T /'terə/
1015 peta P /'petə/
1018 exa E /'eksə/
1021 zetta Z /'zetə/
1024 yotta Y /'jɒtə/
1027 xona X /'zəʊnə/
1030 weka W /'wekə/
1033 vunda V /'vʊndə/

Cardinal Numbers

1 one /wʌn/
2 two /tu:/
3 three /θri:/
4 four /fɔː/
5 five /faɪv/
6 six /sɪks/
7 seven /'sevən/
8 eight /eɪt/
9 nine /naɪn/
10 ten /ten/
11 eleven /ɪ'levən/
12 twelve /twelv/
13 thirteen /θɜ:'ti:n/
14 fourteen /fɔː'ti:n/
15 fifteen /fɪf'ti:n/
16 sixteen /sɪkst'i:n/
17 seventeen /seven'ti:n/
18 eighteen /eɪ'ti:n/
19 nineteen /naɪn'ti:n/
20 twenty /'twentɪ/
21 twenty-one /twentɪ'wʌn/
22 twenty-two /twentɪ'tu:/
23 twenty-three /twentɪ'θri:/
24 twenty-four /twentɪ'fɔː/
25 twenty-five /twentɪ'faɪv/
26 twenty-six /twentɪ'sɪks/
27 twenty-seven /twentɪ'sevən/
28 twenty-eight /twentɪ'eɪt/
29 twenty-nine /twentɪ'naɪn/
30 thirty /'θɜ:tɪ/
40 forty /'fɔːtɪ/
50 fifty /'fɪftɪ/
60 sixty /'sɪkstɪ/
70 seventy /'sevəntɪ/
80 eighty /'eɪtɪ/
90 ninety /'naɪntɪ/
100 a hundred; one hundred /ə 'hʌndrəd/ /wʌn 'hʌndrəd/
101 a hundred and one /ə 'hʌndrəd ən wʌn/
102 a hundred and two /ə 'hʌndrəd ən tu:/
110 a hundred and ten /ə 'hʌndrəd ən ten/
120 a hundred and twenty /ə 'hʌndrəd ən 'twentɪ/
200 two hundred /tu: 'hʌndrəd/
300 three hundred /θri:  'hʌndrəd/
400 four hundred /fɔː 'hʌndrəd/
500 five hundred /faɪv 'hʌndrəd/
600 six hundred /sɪks 'hʌndrəd/
700 seven hundred /'sevən 'hʌndrəd/
800 eight hundred /eɪt 'hʌndrəd/
900 nine hundred /naɪn 'hʌndrəd/
1 000 a thousand, one thousand /ə θ'ɑʊzənd/ /wʌn 'θɑʊzənd/
1 001 a thousand and one /ə 'θɑʊzənd ən wʌn/
1 010 a thousand and ten /ə 'θɑʊzənd ən ten/
1 020 a thousand and twenty /ə 'θɑʊzənd ən 'twentɪ/
1 100 one thousand, one hunded /wʌn 'θɑʊzənd wʌn 'hʌndrəd/
1 101 one thousand, one hundred and one /wʌn 'θɑʊzənd wʌn 'hʌndrəd ən wʌn/
1 110 one thousand, one hundred and ten /wʌn 'θɑʊzənd wʌn 'hʌndrəd ən ten/
9 999 nine thousand, nine hundred and ninety-nine /naɪn 'θɑʊzənd naɪn 'hʌndrəd ən 'naɪntɪ 'naɪn/
10 000 ten thousand /ten 'θɑʊzənd/
15 356 fifteen thousand, three hundred and fifty six /'fɪfti:n 'θɑʊzənd θri: 'hʌndrəd ən 'fɪftɪ sɪks/
100 000 a hundred thousand /ə 'hʌndrəd 'θɑʊzənd/
1 000 000 a million /ə 'mɪljən/
100 000 000 a hundred million /ə 'hʌndrəd 'mɪljən/
1 000 000 000 a billion /ə 'bɪljən/
100 000 000 000 a hundred billion /ə 'hʌndrəd 'bɪljən/
1 000 000 000 000 a trillion /ə 'trɪljən/
1 000 000 000 000 000 a quadrillion /ə kwɒdrɪljən/
1 000 000 000 000 000 000 a quintillian /ə kwɪn'tɪljən/
1 000 000 000 000 000 000 000 a sextillion /ə seks'tɪljən/
1 000 000 000 000 000 000 000 000 a septillion /ə sep'tɪljən/
1 000 000 000 000 000 000 000 000 000 an ocillion /ən ɒkt'tɪljən/
1 000 000 000 000 000 000 000 000 000 000 a nonillion /ə nɒn'ɪljən/
1 000 000 000 000 000 000 000 000 000 000 000 a decillion /ə de'sɪljən/

Ordinal Numbers

1st first /fɜ:st/
2nd second /'sekənd/
3rd third /θɜ:d/
4th fourth /fɔ:θ/
5th fifth /fɪfθ/
6th sixth /sɪksθ/
7th seventh /'sevənθ/
8th eighth /eɪtθ/
9th ninth /naɪnθ/
10th tenth /tenθ/
11th eleventh /ɪ'levənθ/
12th twelfth /'twelfθ/
13th thirteenth /θɜ:'ti:nθ/
14th fourtheenth /fɔː'ti:nθ/
15th fidteenth /fɪf'ti:nθ/   
16th sixteenth /sɪks'ti:nθ/
17th seventeenth /seven'ti:nθ/
18th eighteenth /eɪ'ti:nθ/
19th nineteenth /naɪn'ti:nθ/
20th twentieth /'twentɪəθ/
21st twenty-first /twentɪ'fɜ:st/
22nd twenty-second /twentɪ'sekənd/
23rd twenty-third /twentɪ'θɜ:d/
24th twenty-fourth /twentɪ'fɔ:θ/
25th twenty-fifth /twentɪ'fɪfθ/
26th twenty-sixth /twentɪ'sɪksθ/
27th twenty-seventh /twentɪ'sevənθ/
28th twenty-eighth /twentɪ'eɪtθ/
29th twenty-ninth /twentɪ'naɪnθ/
30th thirtieth /'θɜːtɪəθ/
31st thirty-first /θɜːtɪ'fɜ:st/
40th fortieth /'fɔ:tɪəθ/
50th fiftieth /'fɪftɪəθ/
100th hundredth /'hʌndrədθ/
1 000th thousandth /'θɑʊzəndθ/
1 000 000th miilionth /'mɪljənθ/
Comments