Mathematical Expressions 1

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UNIT 2: MATHEMATICAL EXPRESSIONS AND S

UNITS

LETTERS

It is fundamental to know the whole alphabet in order to read out a formula or mathematical expression. The sound of e

etter is in brackets:

a=/ei/

b= /bi:/

c=/si :/

d=/di:/

e=/i:/ f=/ef/

g=/dzi:/

h=/eitch/

=/ai/

=/dzei/

k=/kei/

=/el/

m=/em/ n=/en/

o=/ou/

p=/pi :/

q=/kju:/

r=/a: (r)/

s=/es/

=/ti:/

u=/ju:/ v=/vi:/

w=/dabelju:/

x=/eks/

y=/wai/

z=/zi:/;/zed/



Numbers

Nº CARDINAL Nº ORDINAL

1 one 1st first

2 two 2nd second

3 three 3rd third

4 four 4th fourth

5 five 5 th fifth

6 six 6 th sixth

7 seven 7 th seventh

8 eight 8 th eighth

9 nine 9 th ninth

10 ten 10 th tenth

11 eleven 11 th eleventh12 twelve 12 th twelfth

13 thirteen 13 th thirteenth

14 fourteen 14 th fourteenth

15 fifteen 15 th fifteenth

16 sixteen 16 th sixteenth

17 seventeen 17 th seventeenth

18 eighteen 18 th eighteenth

19 nineteen 19 th nineteenth

20 twenty 20 th twentieth

21 twenty one 21st twenty first

30 thirty 30 th thirtieth

40 fourty 40 th fortieth

50 fifty 50 th fiftieth

60 sixty 60 th sixtieth

70 seventy 70 th

seventieth80 eighty 80 th eightieth

90 ninety 90 th ninetieth

100 a/one hundred 100 th hundredth

199 a/one hundred,

ninety nine

199 th one hundred,

ninety ninth

1,000/1000 a/one thousand 1,000 th thousandth

1,000,000/1000000 a/one million 1,000,000 th millionth



Mathematical ExpressionsX+Y

X plus Y

X-Y

X minus Y

XxY; XY;X.Y

X multiplied by Y

X timesY

X/Y

Xdivided byY

X over Y

X=YX is equal toY

X equals Y

X<Y

X is less than Y

X>Y

X is more thanY

X is greater than Y

X2

quared

Square X

X3

X cubed

Cubic X

X4

X to the power fourX to the forth power

X to the fourth

X-2

X to the power minus two

X-3

X to the power minus three

X-4



X to the power minus four

ROOTS

he (square) root of X

x

he cube root of X3 x

he fifth root of X5 x

PER:

Per is used when dealing with percentages and also when we talk about physical dimensions:

X%

X per cent

m/seg

metre per second

N/MNewton per metre

VULGAR FRACTIONS

1/2: one/ a half

1/3: one/ a third

1/4: one/ a quarter

1/5: one/ a fifth

4/5: four fifths

DECIMAL FRACTIONS

In English, decimal fractions are represented by a point and not by a comma as in Spanish. We rnust be particularly ca

n this case, because it may lead us to a wrong interpretation (or worse a wrong calculation) of any figure.



The digits following the point should be read one by one. For instance:

15.273 ? is read out fifteen point two, seven, three

When the number "O" comes before the decimal point we can read it out in three different ways. For example 0.489 can

be read:

1. zero point four, eight, nine or

2. nought point four, eight, nine or simply

3. point four, eight, nine

THOUSANDS

We can express thousands by using three different approaches, e.g.:

two thousand, four hundred and fifty three:

1. By using a comma, e.g. 2,453

we must bear in mind that the comma, in English, conveys thousands and not decimal numbers)

2. by leaving a space, e.g. 2 453

3. and without using any sign at all, e.g. 2453

OTHER MATHEMATICAL EXPRESSIONS

N!

N factorial

Logx Y

Logarithm to the base X of Y

The integral of X

dx

Derivative of X



Mathematical Exercise.

Read out:

25, 532 ________________________________________________________________

3. 427 _________________________________________________________________

4532 + 1715 ____________________________________________________________

3, 523 - 2, 148 __________________________________________________________

m

cb

+

−

1 ________________________________________________________________

∫ +++ c xd x x )(________________________________________________________

)(5

t

x

__________________________________________________________________

y = 1

3++ x z

x

____________________________________________________________

4703 = (4 x 103) + (7 x 102) + (0 x 10) + 3 ___________________________________

)!(!

!

r nr

n

−______________________________________________________________

x2 + y2 = z - k ___________________________________________________________

3 )1( − zk ______________________________________________________________

ogx654 _______________________________________________________________



z=+8

1

5

2

______________________________________________________________

200% - 50% = 150% _____________________________________________________

Write down the following mathematical expressions :

One third times eks plus wai _______________________________________________

The root of eks squared plus wai squared minus zed ____________________________

Eks squared plus five halves over two equals minus one half /one over two __________

Wai equals one minus eks over eks squared plus one ____________________________

Eks equals minus bi: plus the root of four times ei over two times ei ________________

Eks to the power six plus three times wai over nine _____________________________

The fifth root of nine plus wai to the power minus seven _________________________

Forty three thousand, five hundred and fifty eight ______________________________

Point three, nine, seven ___________________________________________________

One over the the root of ei squared minus eks squared ___________________________

Ten percent over twenty two percent ________________________________________



SI units

SI units (Système International d'Unités) are a set of internationally agreed units for scientific and technological use. There

even base units and two supplementary units, each with a special name and symbol.

base and supplementary SI unit

PHYSICAL QUANT. NAME OF SI UNIT SYMBOL FOR UNIT

length metre m

mass kilogram(me) Kg

time second s

electric current ampere A

thermodynamic temperature kelvin K

luminous intensity candela cd

amount of substance molean mol

plane angle radian rad

solid angle steradian sr

The units are used with prefixes in front of the word to denote multiples or submultiples of 10. For instance, centi- indicates

0.01), so 1 centimetre (1 cm) is 0.01 metre. Note that the unit of mass is slightly unusual because the base unit is the kilog

not the gram. However, the prefixes are used with "gram" (decigram, etc.).

Decimal Multiples and Submultiples to be used with SI units



MULTIPLE PREFIX SYMBOL SUBMULT. PREFIX SYMBOL

101 deca- da 10-1 deci- d

102 hecto- h 10-2 centi- c

103 kilo- k 10-3 milli- m

106 mega- M 10-6 micro- µ

109 giga- G 10-9 nano- n

1012 tera- T 10-12 pico- p

1015 peta- P 10-15 femto- f

1018 exa- E 10-18 atto- a

DERIVED UNITS are formed by combining base units. Certain units have their own special names and symbols as show

he following table.

Some SI derived units expressed in terms of base units

Quantity SI unit Unit Symbol

Area square metre m2

Volume cubic metre m3

Speed, velocity metre per second m/s

Acceleration metre per second

squared

m/s2

Wave number 1 per metre m-1



Density kilogram per cubic metre Kg/m3

Current Density ampere per square

metre

A/m2

Magnetic field strength ampere per metre A/m

Concentration mole per cubic metre mol/m3

Specific volume cubic metre per

kilogram

m3 /Kg

Luminance candela per square metre

cd/m2

Derived SI units with special names

PHYSICAL QUANTITYNAME OF UNIT SYMBOL

FREQUENCY hertz Hz

ENERGY joule J

FORCE newton N

POWER watt W

PRESSURE pascal Pa

ELECTRIC CHARGE coulomb C



ELECTRIC POTENCIAL

DIFF.

volt V

ELECTRIC RESISTANCE ohm Ω

ELECTRIC

CONDUCTANCE

siemens S

ELECTRIC CAPACITANCE farad F

MAGNETIC FLUX weber Wb

INDUCTANCE henry H

MAGNETIC FLUX

DENSITY

tesla T

LUMINOUS FLUX lumen lm

ILUMINANCE lux lx

ABSORBED DOSE gray Gy

SI UNITSQuantity Unit Symbol Units in

Commom use

Symbol

mass(m) kilogram Kg grammilligram

tonne

g

mg

t



length (l) metre m millimetre

decimetre

centimetre

kilometre

mm

dm

cm

km

area(A)

metre

squared

m2 centimetre

squared

kilometre squaredhectare

cm2

km2

ha

volume(V) metre cubed m3 centimetre cubed

decimetre cubed

litre

millilitre

cm3

dm3

l

ml

density kilogram per

metre cubed

Kg/m3 gram per

centimetre cubed

g/cm3

time second s minute

hour

day

year

min

h

d

frequency hertz Hz kilohertz

megahertz

kHz

MHz

velocity metre per second m/s kilometre per

hour

km/h

accelerat. metre per second

squared

m/s2 centimetre per

second squared

cm/ 2

force newton N

pressure pascal Pa newton per

metre/cm squared

millibar

atmosphere

N/m2

N/cm2

mbar

atm



moment of

force

newton metre Nm

energy heat work joule J kilojoule

megajoule

kilowatt hour

kJ

MJ

kWh

power watt W milliwatt

kilowatt

megawatt

mW

kW

MW

temperat.

(thermod.)

(commom)

kelvin

degree Celsius

K

ºC

electric current ampere A milliamp.

microamp.

mA

µA

electric charge coulomb C

potential

difference

volt V microvolt

millivolt

kilovolt

µV

mV

kV

resistance ohm kilohmmegohm

k M

sound intensity decibel

amount of

substance

mole mol

MATCHING SYMBOLS. Find the symbols in the appendix of this unit which match the following names of units

a. cubic metre ___________________________________________________________

b. metre per second squared _______________________________________________

c. ampere per metre ______________________________________________________

d. yard ________________________________________________________________



e. candela per square metre ________________________________________________

f. Watt ________________________________________________________________

g. Hertz _______________________________________________________________

IMPERIAL UNITS

LENGTH METR. EQUIV.

1 inch 2.54 cm

12 in 1 foot 30.48 cm

3 ft 1 yard 0.9144 m

1760 yd 1 mile 1.6093 km

AREA METR. EQUIV.

1 square inch 6.45 sq cm

144 sq in 1 square foot 0.0929 m2

9 sq ft 1 square yard 0.836 m2

4840 sq yd 1 acre 0.405 ha

640 acres 1 square mile 259 ha

VOLUME METR. EQUIV.

1 cubic inch 16.3871 cm3

1728 cu in 1 cubic foot 0.028 m3



27 cu ft 1 cubic yard 0.765 m3

LIQUID VOLUME

1 pint 0.57 litre

2 pints 1 quart 1.14 litres

4 quarts 1 gallon 4.55 litres

WEIGHT METR. EQUIV.

1 ounce 28.3495 g

16 oz 1 pound 0.4536 kg

14 lb 1 stone 6.35 kg

8 stones 1 hundredweight 50.8 kg

20 cwt 1 ton 1.016 tonnes

4. UNITS.

Write down the full names of the units the following symbols refer to.

a. cm3 _________________________________________________________________

b. kHz _________________________________________________________________

c. km/h ________________________________________________________________

d. kWh ________________________________________________________________

e. A/m2

_______________________________________________________________



f. mol/m3 ______________________________________________________________

g. t ___________________________________________________________________

h. Nm _________________________________________________________________

mA _________________________________________________________________

. mbar ________________________________________________________________

k. ha __________________________________________________________________

dm _________________________________________________________________

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Mathematical Expressions 1