Measurement in science requires correct units, conversion methods, and consistent notation.

1. SI Base Magnitudes (common in 2 ESO)

MagnitudeSI unitSymbol
Lengthmeterm
Masskilogramkg
Timeseconds
TemperaturekelvinK
Electric currentampereA

2. Metric Prefixes

PrefixSymbolFactor
gigaG$10^9$
megaM$10^6$
kilok$10^3$
hectoh$10^2$
decada$10^1$
unit-$10^0$
decid$10^{-1}$
centic$10^{-2}$
millim$10^{-3}$
micromu$10^{-6}$
nanon$10^{-9}$

3. Scientific Notation

Any number can be written as:

$$ a \times 10^b $$

with $1 \le a < 10$ and integer $b$.

Examples:

  • $4200000 = 4.2 \times 10^6$
  • $0.00056 = 5.6 \times 10^{-4}$

4. Unit Conversion by Conversion Factors

Multiply by fractions equal to 1 so units cancel.

Example:

$$ 180\,\mathrm{km/h} \times \frac{1000\,\mathrm{m}}{1\,\mathrm{km}} \times \frac{1\,\mathrm{h}}{3600\,\mathrm{s}} = 50\,\mathrm{m/s} $$

Useful equalities:

  • $1\,\mathrm{L} = 1\,\mathrm{dm^3}$
  • $1\,\mathrm{mL} = 1\,\mathrm{cm^3}$
  • $1\,\mathrm{m^3} = 1000\,\mathrm{L}$

5. Areas and Volumes in Conversions

When converting area and volume, the conversion factor is squared or cubed:

$$ 1\,\mathrm{m^2} = (100\,\mathrm{cm})^2 = 10^4\,\mathrm{cm^2} $$
$$ 1\,\mathrm{m^3} = (100\,\mathrm{cm})^3 = 10^6\,\mathrm{cm^3} $$

6. Geometry Formulas for Volume

ObjectVolume
Cube$V=a^3$
Rectangular prism$V=lwh$
Cylinder$V=\pi r^2 h$
Sphere$V=\frac{4}{3}\pi r^3$
Cone$V=\frac{1}{3}\pi r^2 h$

7. Density and Temperature

Density:

$$ \rho = \frac{m}{V} $$

Temperature conversion:

$$ T(\mathrm{K}) = T(^\circ\mathrm{C}) + 273.15 $$
$$ T(^\circ\mathrm{C}) = T(\mathrm{K}) - 273.15 $$

8. Good Measurement Practice

  • Always include units in final answers.
  • Keep significant figures consistent with data precision.
  • Convert to SI before applying formulas when possible.
  • Check if the final value is physically reasonable.