# SI Units - A Summary

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Learning Objectives

• Know (not memorize) the seven (7) basic quantities and their SI Units.
• Explain what the basic units are.
• Explain what are derived units, and how they are derived.
• Represent all quantities with proper numbers and units whenever possible.

List all the basic quantities and their units you know of and search for those that you do not know yet. Understanding and proper expression of quantities are basic skills for any modern educated person. You have to master all quantities described here.

## The Basic Units

Quantities form the basis for science and engineering and any moment of our lives. Unless you have expressed the quantities in numbers and units, you have not expressed anything. Quantities are defined only when they are expressed in numbers and units. Missing units and improper use of units are serious omissions and errors.

Years ago, physicists used either the mks (meter-kilogram-second) system of units or the cgs (centimeter-gram-second) systems for length, mass, and time. In addition to these three basic quantities are four others: the electric charge or current, temperature, luminous intensity and the amount of substance. Chemical quantities are mostly based on the last one. Thus, these are seven basic quantities, and each has an unit.

The international system of units (Systeme International d'Units) was adopted by the General Conference on Weights and Measure in 1960, and the SI units are widely used today. All SI units are based on these basic units.

Seven Basic Quantities and Units
Quantity Unit Symbol
Length Meter m
Mass Kilogram kg
Time Second s
Electric current Ampere A
Temperature Kelvin K
Luminous intensity Candela cd
Amount of substance Mole mol

Close your eyes, and see if you can name the 7 fundamental quantities in science and their (SI) Units. Science is based on only 7 basic quantities; for each, we have to define a standard unit. Think why these are the basic quantities. Are these related to any other quantities? Can they be derived from other quantities?

## Derived Units

There are other quantities aside from the seven basic quantities mentioned above. However, all other quantities are related to the basic quantities. Thus, their units can be derived from the seven SI units above. For this reason, other units are called derived units The table below lists some examples:

Derived Quantities and Their SI Units

Quantity Unit Symbol
Area square meter m2
Volume cubic meter m3
Density kg per cubic meter kg m-3
Velocity meter per second m s-1
acceleration meter per second per second m s-2

Derived units can be expressed in terms of basic quantities. From the specific derived unit, you can reason its relationship with the basic quantities.

For some specific common quantities, the SI units have special symbols. As you use these often, you will feel at home with them. To remember it is very hard. However, you will encounter them during your study of these quantities. They are collected here to point out to you that these are special SI symbols.

Special Symbols of Some SI Units

Quantity Unit Explanation
Force N Newton = kg m s-2
Pressure Pa Pascal = N m-2
Energy J Joule = N.m
Electric charge C Coulomb = A.s
Electric potential V Volt = J/C
Energy J Joule = N.m
Electric charge C Coulomb = A s
Electric potential V 1 V = 1 J/C
Power watt 1 watt = 1 J/s

## Common Units Still in Use

The following units are still in common use for chemistry. There are some other commonly used units too, but their meanings are clear by the time you use them.

Common Units Still in Use

Quantity Symbol Explanation
Volume L liter = 1 dm3, 1 dm = 0.1 m
mL milliliter = 1/1000 L
Molarity M number of moles dissolved in 1 liter solution
Molality * m number of moles dissolved in 1 kg solvent
* The use of m for molality and for meter is sometimes confusing.

The following units are used in special technologies or disciplines. Since most people are not familiar with them, they are explained in more detail here.

Becquerel
the SI unit for radioactivity symbol (B), which is 1 disintegration per second (dps). 1 Ci = 3.7e10 B.
Curie (Ci)
a unit of radioactivity originally based on the disintegration rate of 1 g of radium. Now a Curie is the quantity of radioactive material that has a disintegration rate of 3.700e10 per second (B). 1 mCi = 1e-3 Ci; 1 microCi = 1e-6 Ci; 1 MCi = 1e6 Ci.
radiation dose units. The gray (Gy) is an SI unit for the absorption of 1 J radiation energy by one kg of material. The rad was a popular unit, which is the absorption of 100 erg of radiation energy by one gram, (1 Gy = 100 rad).
Roentgen (R)
a unit for the measure of X-ray and gamma ray exposure. 1 R = 93 erg per g (1 R = 0.93 rad for X-rays or gamma rays whose energy is above 50 keV).

The unit erg is for energy, 1 J = 10,000,000 erg.

## Review Questions

1. What is the SI unit and symbol for force?

Newton (N), he defined force

One N is the gravitational pull of 98 g mass

1. What is the SI unit and symbol for pressure?

Pascal (Pa), who studied effect of pressure on fluid

1 atm = 101325 Pa = 101.3 kPa

1. What physical quantity uses the unit Joule?

Joule (J) is an energy unit

1 J = 1 N m = 10e7 ergs

1. Which is the SI unit for temperature?

Kelvin (K)

1C is the same as 273.15 K

1. What is the SI unit for measuring the amount of substance?

mole (mol), derived from Latin, meaning mass

one mole has 6.023e23 atoms or molecules

1. What are the symbols for the seven basic SI units?

m, kg, s, A, K, cd, mol

m, k, s, current, temperature, luminous, mole

1. What is the unit M used for?

M stands for mol/L, a concentration unit

1. What is the unit A used for?

1 C/s, for an electric current

1. What is the power consumption if the current is 1 A from a source of 10 V?

10 C/s V (J/s = watt)

watt is the unit for power

1. What is the SI unit for measuring radioactivity?