﻿ Lab Math |

### Converting Units

1. Write the conversion as an equation: starting number (starting units) ¼ new number (new units):
2. Count the number of different units in the equation. Numbers and Measurements in the Laboratory 23
3. Add that many empty fractions to the left-hand side of the equation.
4. Start to fill in those fractions by adding whatever units you need to cancel the old units and adding whatever units you need to make the new units appear.
5. Make the fractions equal to 1 (turn them into unit fractions).
6. Multiply.

### Measuring Fundamental Properties

Fundamental propertySymbol for propertyDimensionSI unitSymbol for unit
Amount of substancenNmolemol
Lengthl, dLmeterm
MassmMkilogramkg
Timet, τTsecondsec
TemperatureTqkelvinK
Electric currentIAampereA
Luminous intensityIvJcandelacd

#### Amount of a Substance

Dimension: N.
SI Unit: Moles (mol).
Physical Basis: A mole is the number of atoms in 12 g of carbon-12 (12C). That number is \$6.02 × 1023\$

#### Length

Dimension: L.
SI Unit: Meters (m).
Physical Basis: A meter is defined as the distance that light travels in a vacuum in \$1/299792458\$ of a second.

#### Mass

Dimension: M.
SI Unit: Kilogram (kg).
Physical Basis: A kilogram is based on the international prototype of kilogram.

#### Time

Dimension: T.
SI Unit: Second (sec).
Physical Basis: A second is defined as the amount of time it takes for a cesium-133 (133Cs) atom to transition between two hyperfine levels of the ground state 9,192,631,770 times.

#### Temperature

Dimension: Q.
SI Unit: Kelvin (K).
Physical Basis: A kelvin is the fraction \$1/273.16\$ of the thermodynamic temperature of the triple point of water.

Converting to Kelvin:
\$K = ^oC + 273\$,
\$K = ({^oF - 32})({5/9})+273\$

Converting to Celsius:
\$^oC = K - 273\$,
\$^oC = ({^oF - 32})({5/9})\$

#### Electric Current

Dimension: A.
SI Unit: Ampere (A).
Physical Basis: The ampere is that constant current, which, if maintained in two straight parallel conductors of infinite length or negligible circular cross section and placed 1 m apart in a vacuum, would produce between these conductors a force equal to \$({2 × 10^{−7}}) N\$ per meter of length. (An ampere is the amount of current that would be produced by an electromotive force of 1 V acting through a resistance of 1 Ω.)

#### Luminous Intensity

Dimension: J.
SI Unit: Candela (cd).
Physical Basis: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency \$540 × 10^12\$ hertz (Hz) and that has a radiant intensity in that direction of 1/683 watt (W) per steradian (sr).

## Reference Tables and Equations

GREEK SYMBOLS

Greek

Computer key

(United States pronunciation) And some standard uses of uppercase and lowercase symbols

A α

alpha

A a

Cutoff for statistical significance

B β

beta

B b

(1 – β) is the power of a statistical test.

Γ γ

gamma

G g

Micrograms

Δ δ

delta

D d

CHANGE IN; change in

E ɛ

epsilon

E e

Z ζ

zeta

Z z

(“zate-ah”)

H η

eta

H h

(“ate-ah”) Symbol for viscosity

Θ θ

theta

Q q

(“thate-ah”)

I ι

iota

I i

K κ

kappa

K k

Λ λ

lambda

L l

Microliters Symbol for wavelength

M μ

mu

M m

(“myoo”) Micro-Symbol for population mean

N ν

nu

N n

Symbol for frequency

Ξ ξ

xi

X x

(“zi” or “k-sigh”)

O ο

omicron

O o

Π π

pi

P p

3.1416; the circumference of a circle divided by its diameter

P ρ

rho

R r

Symbol for density

Σ σ

sigma

S s

SUM; symbol for population standard deviation

T τ

tau

T t

Time constant

Y υ

upsilon

U u

Φ φ

phi

F f

(“fee”)

X χ

chi

C c

(“ki”)

Ψ ψ

psi

Y y

(“sigh”)

Ω ω

omega

W w

SYMBOL FOR OHMS; symbol for angular frequency

PREFIXES FOR UNITS

Prefix

Abbreviation

Multiplier

yotta-

Y

1024

zetta-

Z

1021

exa-

E

1018

peta-

P

1015

tera-

T

1012

giga-

G

109

mega-

M

106

kilo-

k

103

hecto-

h

102

deca-

da

101

deci-

d

10−1

centi-

c

10−2

milli-

m

10−3

micro-

μ

10−6

nano-

n

10−9

pico-

p

10−12

femto-

f

10−15

atto-

a

10−18

zepto-

z

10−21

yocto-

y

10−24

PREFIXES FOR NOMENCLATURE

Prefix

Multiplier

hemi-

1/2

mono-

1

di-, bi-, bis-

2

tri-, tris-

3

tetra-

4

penta-

5

hexa-

6

hepta-

7

octa-

8

nona-

9

deca-

10

SYSTÈME INTERNATIONALE UNITS: SI UNITS

Property

Symbol for property

Dimension

SI unit

Symbol for unit

Symbol in base units

Length

l, d

L

meter

m

m

Mass

m

M

kilogram

kg

kg

Time

t, τ

T

second

s

s

Electric current

I

A

ampere

A

A

Temperature

T

Θ

kelvin

K

K

Amount of substance

n

N

mole

mol

mol

Luminous intensity

IV

J

candela

cd

cd

Plane angle

α

m m−1

Solid angle

Ω

sr

m2 m−2

Area

A

L2

meters squared

m2

m2

Volume

V

L3

meters cubed

m3

m3

Volume

L3

liter

l or L

10−3 m3

Frequency

f

T −1

hertz

Hz

s−1

T −1

becquerel

Bq

s−1

Rate, speed, velocity

U, ν

L T −1

meters/second

m s−1

m s−1

Angular velocity

ω

T −1

m m−1 s−1

Acceleration

a

L T −2

meters/second squared

m s−2

m s−2

Molarity

M

N L−3

mol/liter

M

mol 103 m−3

Density

ρ

M L−3

kilograms/meter cubed

kg m−3

kg m−3

Concentration

c

M L−3

kilograms/liter

kg L−1

kg 103 m−3

Force, weight

F, w

M L T −2

newton

N

kg m s−2

Pressure

p

M L−1 T −2

pascal

Pa; N m−2

kg m−1 s−2

Energy, work

E, W

M L2 T −2

joule

J; N m

kg m2 s−2

Power

P

M L2 T −3

watt

W; J s−1

kg m2 s−3

Electrical charge

Q

T A

coulomb

C

s A

Electrical potential

V

M L2 T −3 A−1

volt

V; W A−1

kg m2 s−3 A−1

Electrical resistance

R, Ω

M L2 T −3 A−2

ohm

Ω; V A−1

kg m2 s−3 A−2

Electrical capacitance

C

M−1 L−2 T 4 A2

F; C V−1

kg−1 m−2 s4 A2

Electrical field strength

M L T −3 A−1

volts/meter

V m−1

kg m s−3 A−1

Inductance

M L2 T −2 A−2

henry

H; Wb A−1

kg m2 s−2 A−2

Conductance

M−1 L−2 T3 A2

siemen

S; A V−1

kg−1 m−2 s3 A2

Flux density

MT −2 A−1

tesla

T; Wb m−2

kg s−2 A−1

Magnetic flux

M L2 T −2 A−1

weber

Wb, V s

kg s−2 A−1 m2

Luminous flux

J

lumen

lm; cd sr

cd

Illuminance

L−2 J

lux

lx; lm m−2

m−2 cd

Luminance

L−2 J

candelas/meter squared

cd m−2

m−2 cd

Heat capacity/entropy

S

M L2 T −2 Θ−1

joules/kelvin

J K−1

kg m2 s−2 K−1

Specific entropy

L2 T −2 Θ−1

joules/kilogram kelvin

J kg−1 K−1

m2 s−2 K−1

Thermal conductivity

M L T −3 Θ−1

watts/meter kelvin

W kg−1 K−1

kg m s−3 K−1

The seven fundamental units (SI base units) are assumed to be mutually independent; that is, none of the base units can be constructed by arranging any of the others. The fundamental units are shown in boldface letters.

OTHER UNITS

Property

Symbol for property

Dimensions

Other unit

Symbol for unit

To convert to SI

Plane angle

θ, α

degree

°

Mass

m

M

dalton

D

kg = D ÷ (6.022142 × 1026)

Temperature

T

Θ

degree Celsius

°C

K = °C + 273.15

Temperature

T

Θ

degree Fahrenheit

°F

K = (5/9)°F + 255.37

Area

A

L2

hectare

ha

m2 = 0.0001 ha

Volume

V

L3

cubic cm

cc

mL = cc

Force

F

M L T −2

dyne

dyn

N = 105 dyne

Pressure

p

M L−1 T −2

atmosphere

atm

Pa = 9.86926 × 10−6 atm

Energy, work

E, W

M L2 T −2

calorie

cal

J = 0.239 cal

Energy, work

E, W

M L2 T −2

erg

erg

J = 107 erg