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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/ |
log₂x |
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 |
x² |
x squared |
x³ |
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 |
ẋ |
x dot |
ẍ |
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 |
dvdθ |
d v by d theta, the derivative of v with respect to theta |
d²vdθ² |
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. |
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 |
limΔx→0 |
the limit as delta x approaches zero, the limit as delta x tends to zero |
LtΔx→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/ |
⅓ |
a third |
/ə 'θɜ:d/ |
⅔ |
two thirds |
/tu: 'θɜ:dz/ |
⅕ |
a fifth |
/ə 'fɪfθ/ |
⅖ |
two fifths |
/tu: 'fɪfθs/ |
⅗ |
three fifths |
/θriː 'fɪfθs/ |
⅘ |
four fifths |
/fɔː 'fɪfθs/ |
⅙ |
a sixth |
/ə 'sɪksθ/ |
⅚ |
five sixths |
/faɪv 'sɪksθs/ |
⅛ |
an eighth |
/ən 'eɪtθ/ |
⅜ |
three eighths |
/θriː 'eɪtθs/ |
⅝ |
five eighths |
/faɪv 'eɪtθs/ |
⅞ |
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 |
millionth |
/'mɪljənθ/ |