SPI Physics · Units, Measurement and Dimensions

SI Units, Prefixes and Conversions

SI has seven base units such as the metre, kilogram and second; other units like the newton and joule are built from them, prefixes such as milli and micro scale them by powers of ten, and CGS units convert to SI the same way.

All Units, Measurement and Dimensions notes

Why this matters

Five questions in the bank, all EASY, and two of them are from the 2022 paper: the joule in ergs and the newton in dynes. The others ask the SI unit of mass, the unit of frequency, and the values of mA and μA. Every one is a unit name or a power of ten, so the tables here are the whole job.

Concept 1 of 3: SI base units and derived units

SI picks one unit for each basic quantity: length, mass, time and four more. Every other unit is made by multiplying or dividing these, so a newton is really a kilogram metre per second squared.

Definition

SI has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela.
Derived units are built from them: speed in m/s, force in newtons, energy in joules.
The SI unit of mass is the kilogram, not the gram. Quintal (100 kg) and tonne (1000 kg) are trade units.
Frequency is oscillations per second, so its unit, the hertz, is $\text{s}^{-1}$ .

Quantity	SI unit	Symbol and meaning
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd
Force	newton	N, which is kg m/s²
Work and energy	joule	J, which is N m
Power	watt	W, which is J/s
Frequency	hertz	Hz, which is per second (s⁻¹) Per second, not second and not second squared.
Pressure	pascal	Pa, which is N/m²

The first seven rows are the base units; the rest are derived from them.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 1 · Units, Measurement and Dimensions · SI Units, Prefixes and Conversions

Standard unit of measuring mass is called

The gram as the SI unit of mass

The SI unit of mass is the kilogram. The gram is one thousandth of it and belongs to the CGS system.

Celsius as the SI unit of temperature

The SI base unit of temperature is the kelvin. The degree Celsius is in daily use, but it is not the SI unit.

Drill 1 more on si base units and derived units

Concept 2 of 3: Prefixes: powers of ten

A prefix is a short way to write a power of ten in front of a unit. A kilometre is a thousand metres; a milliampere is a thousandth of an ampere. Learn the ladder once and every conversion is a shift of the decimal point.

Definition

Big prefixes multiply: kilo ( $10^3$ ), mega ( $10^6$ ), giga ( $10^9$ ).
Small prefixes divide: centi ( $10^{-2}$ ), milli ( $10^{-3}$ ), micro ( $10^{-6}$ ), nano ( $10^{-9}$ ).
Capital M is mega; small m is milli. The Greek letter μ is micro.

Prefix	Symbol	Value
giga	G	$10^9$
mega	M	$10^6$
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$ Micro is a thousand times smaller than milli.
nano	n	$10^{-9}$

Each step from kilo down to nano (missing out centi) is a factor of 1000.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 2 · Units, Measurement and Dimensions · SI Units, Prefixes and Conversions

The values of mA and

\mu

A are

Swapping milli and micro

Milli is

10^{-3}

and micro is

10^{-6}

. A microampere is a thousandth of a milliampere.

Reading capital M as milli

Capital M is mega (

10^6

); small m is milli (

10^{-3}

). 1 MW is a million watts, not a thousandth of a watt.

Concept 3 of 3: Converting CGS units to SI

The CGS system uses the centimetre, the gram and the second. Its units are smaller than the SI ones, so one SI unit equals many CGS units. Write the SI unit in kilograms and metres, swap each for grams and centimetres, and multiply out.

Definition

$1\text{ kg} = 1000\text{ g} = 10^3\text{ g}$ and $1\text{ m} = 100\text{ cm} = 10^2\text{ cm}$ .
Force: $1\text{ N} = 1\text{ kg m/s}^2 = 10^3\text{ g} \times 10^2\text{ cm/s}^2 = 10^5$ dyne.
Work and energy: $1\text{ J} = 1\text{ N} \times 1\text{ m} = 10^5\text{ dyne} \times 10^2\text{ cm} = 10^7$ erg.
For an area or volume, convert each length: $1\text{ m}^2 = 10^4\text{ cm}^2$ , $1\text{ m}^3 = 10^6\text{ cm}^3$ .

CGS and SI

1\text{ N} = 10^5\text{ dyne} \qquad 1\text{ J} = 10^7\text{ erg} \qquad 1\text{ m}^2 = 10^4\text{ cm}^2

Worked example

The SI unit of pressure is the pascal, 1 N/m². Express 1 Pa in dyne per square centimetre.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SPI · 2022 · SPI Entrance Examination 2022 · Q88Easy

Example 3 · Units, Measurement and Dimensions · SI Units, Prefixes and Conversions

One joule of work is equal to____erg.

Converting an area with the length factor

1 m is 100 cm, but 1 m² is

100 \times 100 = 10^4

cm², not 100 cm².

Getting the direction backwards

The SI unit is the bigger one: one newton is

10^5

dynes, so a dyne is

10^{-5}

N, not

10^5

Mixing up dyne and erg

The dyne is the CGS unit of force and the erg is the CGS unit of energy. They pair with the newton and the joule.

Drill 1 more on converting cgs units to si

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Converting CGS units to SI
CGS and SI
$1\text{ N} = 10^5\text{ dyne} \qquad 1\text{ J} = 10^7\text{ erg} \qquad 1\text{ m}^2 = 10^4\text{ cm}^2$

Reference tables (2)

SI base units and derived units12 rows

Quantity	SI unit	Symbol and meaning
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd
Force	newton	N, which is kg m/s²
Work and energy	joule	J, which is N m
Power	watt	W, which is J/s
Frequency	hertz	Hz, which is per second (s⁻¹) Per second, not second and not second squared.
Pressure	pascal	Pa, which is N/m²

The first seven rows are the base units; the rest are derived from them.

Prefixes: powers of ten7 rows

Prefix	Symbol	Value
giga	G	$10^9$
mega	M	$10^6$
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$ Micro is a thousand times smaller than milli.
nano	n	$10^{-9}$

Each step from kilo down to nano (missing out centi) is a factor of 1000.

Watch out for (7)

The gram as the SI unit of mass
→ SI base units and derived units
Celsius as the SI unit of temperature
→ SI base units and derived units
Swapping milli and micro
→ Prefixes: powers of ten
Reading capital M as milli
→ Prefixes: powers of ten
Converting an area with the length factor
→ Converting CGS units to SI
Getting the direction backwards
→ Converting CGS units to SI
Mixing up dyne and erg
→ Converting CGS units to SI

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