How to read numbers, figures and mathematical expressions
in English.
Cardinal numbers
Cardinal numbers refer to the size of a group.
1
2
3
4
zero
(nought)
one
two
three
four
5
five
15
6
7
8
9
six
seven
eight
nine
16
17
18
19
0
10 ten
11
12
13
14
eleven
twelve
thirteen
fourteen
fifteen (note "f", not
"v")
sixteen
seventeen
eighteen (only one "t")
nineteen
20 twenty
30 thirty
40 forty (no "u")
50 fifty (note "f", not "v")
60
70
80
90
sixty
seventy
eighty (only one "t")
ninety (note the "e")
If a number is in the range 21 to 99, and the second digit is not zero, one
should write the number as two words separated by a hyphen.
21 twenty-one
25 twenty-five
32 thirty-two
58 fifty-eight
64 sixty-four
79 seventy-nine
83 eighty-three
99 ninety-nine
In English, the hundreds are perfectly regular, except that the word hundred
remains in its singular form regardless of the number preceding it
(nevertheless, one may on the other hand say "hundreds of people flew in", or
the like)
100 one hundred
200 two hundred
… …
900 nine hundred
“English for Economists I” – Dr T.Tseligka-Gkaziani (Senior Teaching Fellow in
ESP/EAP). University of Ioannina.
1
So too are the thousands, with the number of thousands followed by the word
"thousand"
1,000
2,000
…
10,000
11,000
…
20,000
21,000
30,000
85,000
100,000
one thousand
two thousand
…
ten thousand
eleven thousand
…
twenty thousand
twenty-one thousand
thirty thousand
eighty-five thousand
one hundred thousand
nine hundred and ninety-nine thousand (British English)
999,000
nine hundred ninety-nine thousand (American English)
1,000,000 one million
10,000,000 ten million
Ordinal numbers
Ordinal numbers refer to a position in a series. Common ordinals include:
zeroth or noughth (see
below)
1st first
0th
2nd second
3rd
4th
5th
6th
7th
8th
9th
third
fourth
fifth
sixth
seventh
eighth (only one "t")
ninth (no "e")
10th tenth
11th eleventh
twelfth (note "f", not
12th
"v")
13th thirteenth
14th fourteenth
15th fifteenth
16th sixteenth
17th seventeenth
18th eighteenth
19th nineteenth
20th twentieth
30th thirtieth
40th fortieth
50th fiftieth
60th sixtieth
70th seventieth
80th eightieth
90th ninetieth
Zeroth only has a meaning when counts start with zero, which happens in a
mathematical or computer science context.
“English for Economists I” – Dr T.Tseligka-Gkaziani (Senior Teaching Fellow in
ESP/EAP). University of Ioannina.
2
Ordinal numbers such as 21st, 33rd, etc., are formed by combining a cardinal
ten with an ordinal unit.
21st twenty-first
25th twenty-fifth
32nd thirty-second
58th fifty-eighth
64th sixty-fourth
79th seventy-ninth
83rd eighty-third
99th ninety-ninth
[The sections on Cardinal and Ordinal Numbers have been adapted from:
http://www.wikipedia.org)
Addition, subtraction, multiplication, division








x+y
x–y
x±y
a y
x:y
x/y
x (a+b)
(a+b) x
x plus y
x minus y
x plus [or] minus y
a times y / a multiplied by y
x divided by y
x over y
x times the sum of a and b
open parenthesis a plus b close parenthesis
multiplied by x
Decimals
 4.59
 0.73
 0.666…
four point five nine
zero point seven three
zero point six recurring
Fractions
 ½
 1/3
 2/3
 ¼
 ¾
 1/5
one (or: a) half
one (or: a) third
two thirds
one (or: a) quarter
three quarters
one(or: a) fifth
For larger numbers we usually say:
 3/7
three sevenths or three over seven
 4/10
four tenths or four over ten
 121/298
one hundred and twenty-one over two hundred
and ninety-eight
“English for Economists I” – Dr T.Tseligka-Gkaziani (Senior Teaching Fellow in
ESP/EAP). University of Ioannina.
3
When fractions are found together with integer, they are read as follows:
 8 3/8
eight and three eighths
 5½
five and a half
Powers, roots
 5²
 8³
 6ⁿ
 7n






91/2
2
3
2
n
2
 b
( x  y)2
Equations
 10+15=25
 x≡y
 x y
 x≈y
 x≠y
 x >y
 x≥y
 x <y
 x≤y
 0  x 1
 0  x 1
Functions
 f ( x)
 f :S T
 x
 x
 f ( x )

f ( x )

dy
dx
f ( x )
x1

5 squared
8 cubed / 8 to the third power
6 to the ninth (power) / 6 to the power n / 6 to the n
7 to the minus nth power/ 7 to the power minus n/
7 to the minus n
9 to (the) half power / the square root of 9
the square root of two
the cube root of two
The nth root of two
the square root of the sum of a plus b
x plus y all squared
ten plus fifteen equals (or: is equal to) twenty-five
x is identical with (or: to) y
x is equivalent to y (set theory)
x is nearly/approximately equal to y
x is not equal to y
x is greater (or: more) than y
x is greater (or: more) or than or equal to y
x is smaller (or: less) than y
x is less (or: smaller) than or equal to y
zero is less than x is less than one
zero is less than or equal to x is less than or equal
to one
fx / f of x / the function f of x
a function f from S to T
x prime
x double prime
f prime x / f dash x / the first derivative of f with
respect to x
f double-prime x / f double-dash x / the second
derivative of f with respect to x
the derivative of y with respect to x
the partial (derivative) of f with respect to x1
“English for Economists I” – Dr T.Tseligka-Gkaziani (Senior Teaching Fellow in
ESP/EAP). University of Ioannina.
4

 2 f ( x)
x12
the second partial (derivative) of f with respect to
x1


the integral from zero to infinity
∫∫
∫∫∫
lim
double integral
triple integral
the limit as x approaches zero
lim
the limit as x approaches zero from above
lim
the limit as x approaches zero from below


ln y
log x
log y to the base e / natural log (of) y
the log of x

log10 x
the common log of x

log2 x
the binary log of x/ the log of x to the base two

0





x 0
x  0
x  0
Linear Algebra
 AT
 A1
A transpose / the transpose of A
A inverse / the inverse of A
Sets






x A
x A
A B
A B
A B
A B
x belongs to A / x is an element of A
x does not belong to A / x is not an element of A
A is contained in B / A is a subset of B
A cap B / A meet B / A intersection B
A cup B / A join B / A union B
A cross B / the Cartesian product of A and B
Logic




x
x
pq
pq
there exists x
for all x
p implies q / if p, then q
p if and only if q / p is equivalent to q
Various
 1….10
 -3
 ∞
 [x]
 -x
 x
one to ten
minus [negative] 3
infinity
x in brackets
minus [negative] x
x tilde
“English for Economists I” – Dr T.Tseligka-Gkaziani (Senior Teaching Fellow in
ESP/EAP). University of Ioannina.
5

X
N (0,1)



x
xi
xi
the stochastic (random) variable X has the
standard normal distribution.
x bar
x super i
xi / x subscript i / x suffix i / x sub i


x̂
x
x hat / x wedge
mod x / modulus x / absolute value of x

x
norm of x

n!
n factorial

X
N
i 1
i
the sum of X sub i from i equals 1 to N / the sum
as i runs from 1 to N of the X sub i

even vs odd numbers
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Acknowledgements
Special thanks are owed to Athanasios Lapatinas (Lecturer, Dept.of Economics,
Ioannina) for his useful contributions and review of the handout.
“English for Economists I” – Dr T.Tseligka-Gkaziani (Senior Teaching Fellow in
ESP/EAP). University of Ioannina.
6