Unit Systems: Measurement in Scientific Work - Physics (Grade 10)

Numbers Need a Shared Language

Imagine reading the measurement result $12$ without a unit. Is it $12 \text{ cm}$ , $12 \text{ m}$ , $12 \text{ kg}$ , or $12 \text{ s}$ ? The number is the same, but the meaning can change completely.

A unit is a reference size used to compare a quantity. In physics, units make measurements from different people, tools, and places readable in the same language.

\text{measurement result} = \text{measured value} \times \text{unit}

The measured value answers how much. The unit answers which reference it is compared with.

From Many Systems to SI

Before one standard became widely used, several unit systems existed side by side. Three names often appear in physics books:

System	Example base units	How to read them
FPS	$\text{ft},\ \text{lb},\ \text{s}$	foot, pound, and second
CGS	$\text{cm},\ \text{g},\ \text{s}$	centimeter, gram, and second
MKS	$\text{m},\ \text{kg},\ \text{s}$	meter, kilogram, and second

These differences make measurements hard to compare when the unit system is unclear. That is why modern science uses the International System of Units or SI. SI comes from the French name Système international d'unités. BIPM, the International Bureau of Weights and Measures, is the international organization that maintains the SI standard.

The official BIPM source for measurement units can be opened through bipm.org.

SI is not just a list of abbreviations. SI is an agreement that $1 \text{ m}$ , $1 \text{ kg}$ , and $1 \text{ s}$ mean the same thing in different schools, laboratories, factories, and countries.

The Seven SI Base Units

SI base units are the building blocks. From them, other units such as $\text{m}^2$ , $\text{m/s}$ , $\text{N}$ , $\text{J}$ , and $\text{W}$ are built.

Base quantity	Common symbol	SI unit	Unit symbol	Dimension
Length	$\ell,\ x,\ r$	meter	$\text{m}$	$[\mathrm{L}]$
Mass	$m$	kilogram	$\text{kg}$	$[\mathrm{M}]$
Time	$t$	second	$\text{s}$	$[\mathrm{T}]$
Electric current	$I$	ampere	$\text{A}$	$[\mathrm{I}]$
Thermodynamic temperature	$T$	kelvin	$\text{K}$	$[\Theta]$
Amount of substance	$n$	mole	$\text{mol}$	$[\mathrm{N}]$
Luminous intensity	$I_v$	candela	$\text{cd}$	$[\mathrm{J}]$

One detail often causes confusion: the SI base unit for mass is $\text{kg}$ , not $\text{g}$ . So when mass is written in grams, convert it to kilograms if you want the full SI base unit form.

\begin{aligned} 1 \text{ g} &= 10^{-3} \text{ kg} \\ 250 \text{ g} &= 250 \times 10^{-3} \text{ kg} = 0.25 \text{ kg} \end{aligned}

Derived Units Come from Operations

A derived unit appears when a derived quantity is formed from base quantities. If the formula multiplies or divides quantities, the units are multiplied or divided too.

Derived quantity	Quantity formula	SI unit	Dimension
Area	$A = l \times w$	$\text{m}^2$	$[\mathrm{L}]^2$
Volume	$V = l \times w \times h$	$\text{m}^3$	$[\mathrm{L}]^3$
Density	$\rho = \frac{m}{V}$	$\text{kg/m}^3$	$[\mathrm{M}][\mathrm{L}]^{-3}$
Speed	$v = \frac{\Delta s}{\Delta t}$	$\text{m/s}$	$[\mathrm{L}][\mathrm{T}]^{-1}$
Acceleration	$a = \frac{\Delta v}{\Delta t}$	$\text{m/s}^2$	$[\mathrm{L}][\mathrm{T}]^{-2}$
Force	$F = m \times a$	$\text{N}$	$[\mathrm{M}][\mathrm{L}][\mathrm{T}]^{-2}$
Work	$W = F \times \Delta s$	$\text{J}$	$[\mathrm{M}][\mathrm{L}]^2[\mathrm{T}]^{-2}$
Power	$P = \frac{W}{t}$	$\text{W}$	$[\mathrm{M}][\mathrm{L}]^2[\mathrm{T}]^{-3}$

The chain of a derived unit shows where it came from. For example, force uses the unit newton, but a newton is built from kilogram, meter, and second.

\begin{aligned} F &= m \times a \\ 1 \text{ N} &= 1 \text{ kg} \cdot \text{m/s}^2 \\ &= 1 \text{ kg m s}^{-2} \end{aligned}

Once force is clear, work and power can be read step by step.

\begin{aligned} 1 \text{ J} &= 1 \text{ N} \cdot \text{m} = 1 \text{ kg m}^2\text{ s}^{-2} \\ 1 \text{ W} &= \frac{1 \text{ J}}{1 \text{ s}} = 1 \text{ kg m}^2\text{ s}^{-3} \end{aligned}

Metric Prefixes Save Zeros

When a size is very large or very small, we do not need to write long rows of zeros. SI uses metric prefixes to express powers of $10$ .

mermaid

Common prefixes include:

Factor	Prefix	Symbol	Factor	Prefix	Symbol
$10^1$	deca	$\text{da}$	$10^{-1}$	deci	$\text{d}$
$10^2$	hecto	$\text{h}$	$10^{-2}$	centi	$\text{c}$
$10^3$	kilo	$\text{k}$	$10^{-3}$	milli	$\text{m}$
$10^6$	mega	$\text{M}$	$10^{-6}$	micro	$\mu$
$10^9$	giga	$\text{G}$	$10^{-9}$	nano	$\text{n}$
$10^{12}$	tera	$\text{T}$	$10^{-12}$	pico	$\text{p}$
$10^{15}$	peta	$\text{P}$	$10^{-15}$	femto	$\text{f}$
$10^{18}$	exa	$\text{E}$	$10^{-18}$	atto	$\text{a}$
$10^{21}$	zetta	$\text{Z}$	$10^{-21}$	zepto	$\text{z}$
$10^{24}$	yotta	$\text{Y}$	$10^{-24}$	yocto	$\text{y}$

Scope note: the list above follows prefixes commonly used in grade $10$ material. BIPM also lists newer SI prefixes that go larger and smaller, such as $10^{30}$ and $10^{-30}$ .

The official BIPM source for SI prefixes can be opened through bipm.org.

Reading Prefixes in Calculations

A prefix is attached to a base unit. For example, $\text{km}$ means kilo-meter, not a separate unit unrelated to the meter.

\begin{aligned} 7.5 \text{ km} &= 7.5 \times 10^3 \text{ m} \\ &= 7500 \text{ m} \end{aligned}

For small sizes, prefixes keep writing compact. A diameter of $0.1 \ \mu\text{m}$ is equal to:

\begin{aligned} 0.1 \ \mu\text{m} &= 0.1 \times 10^{-6} \text{ m} \\ &= 1.0 \times 10^{-7} \text{ m} \end{aligned}

The extremely small mass of an electron is also easier to read with scientific notation.

9.11 \times 10^{-31} \text{ kg}

The point is not to memorize every prefix at once. When you see a unit such as $\text{cm}$ , $\text{mg}$ , or $\mu\text{m}$ , first separate the prefix from the base unit. Then convert the prefix into a power of $10$ and continue the calculation.