Base and Non-Base Unit Conversions

Base units are the fundamental units of measurement in the International System of Units (SI).
Examples include meter (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.
These units are defined independently and are not derived from other units.

Non-base units, also known as derived units, are formed by combining base units through multiplication or division.
Examples include square meter (m²) for area, cubic meter (m³) for volume, meter per second (m/s) for speed, kilogram per cubic meter (kg/m³) for density, and newton (N) for force.

Conversion factors are ratios that express how many of one unit are equal to another unit.
They are used to change measurements from one unit to another.
For example, 1 meter (m) = 100 centimeters (cm), so the conversion factor to change meters to centimeters is 100 cm/m.
When converting, multiply the original measurement by the conversion factor to cancel out the original unit and introduce the new unit.

To convert from base units to non-base units, identify the relationship between the units involved.
For example, to convert from meters (base unit) to kilometers (non-base unit), use the relationship 1 km = 1000 m.
Divide the number of meters by 1000 to get the equivalent value in kilometers
Similarly, to convert from seconds (base unit) to hours (non-base unit), use the relationship 1 hour = 3600 seconds.
Divide the number of seconds by 3600 to get the equivalent value in hours.

To convert from non-base units to base units, identify the relationship between the units involved.
For example, to convert from kilometers (non-base unit) to meters (base unit), use the relationship 1 km = 1000 m.
Multiply the number of kilometers by 1000 to get the equivalent value in meters.
Similarly, to convert from hours (non-base unit) to seconds (base unit), use the relationship 1 hour = 3600 seconds.
Multiply the number of hours by 3600 to get the equivalent value in seconds.

For area conversions, square the conversion factor for length.
For example, to convert from square meters (m²) to square centimeters (cm²), use the relationship 1 m = 100 cm.
Square both sides: (1 m)² = (100 cm)², which gives 1 m² = 10,000 cm².
Multiply the number of square meters by 10,000 to get the equivalent value in square centimeters.
For volume conversions, cube the conversion factor for length.
For example, to convert from cubic meters (m³) to cubic centimeters (cm³), use the relationship 1 m = 100 cm.
Cube both sides: (1 m)³ = (100 cm)³, which gives 1 m³ = 1,000,000 cm³.
Multiply the number of cubic meters by 1,000,000 to get the equivalent value in cubic centimeters.

Density is mass per unit volume, typically expressed in kg/m³ (base units) or g/cm³ (non-base units).
To convert density from g/cm³ to kg/m³, use the relationships 1 kg = 1000 g and 1 m³ = 1,000,000 cm³.
Multiply the density in g/cm³ by (1 kg / 1000 g) and (1,000,000 cm³ / 1 m³) which simplifies to multiplying by 1000.
To convert density from kg/m³ to g/cm³, multiply the density in kg/m³ by (1000 g / 1 kg) and (1 m³ / 1,000,000 cm³) which simplifies to dividing by 1000.

Speed is distance per unit time, typically expressed in m/s (base units) or km/h (non-base units).
To convert speed from m/s to km/h, use the relationships 1 km = 1000 m and 1 h = 3600 s.
Multiply the speed in m/s by (3600 s / 1 h) and (1 km / 1000 m) which simplifies to multiplying by 3.6.
To convert speed from km/h to m/s, multiply the speed in km/h by (1 h / 3600 s) and (1000 m / 1 km) which simplifies to dividing by 3.6.

Metric prefixes are used to denote multiples or fractions of base units, forming non-base units.
Common prefixes include kilo (k) for 1000, centi (c) for 0.01, and milli (m) for 0.001.
For example, 1 kilometer (km) = 1000 meters (m), 1 centimeter (cm) = 0.01 meters (m), and 1 millimeter (mm) = 0.001 meters (m).
When converting between prefixed units, use the prefix value as a conversion factor

Convert 5 g/cm³ to kg/m³.
Use the relationship 1 g/cm³ = 1000 kg/m³.
Multiply 5 g/cm³ by 1000 kg/m³ per g/cm³: 5 g/cm³ * (1000 kg/m³)/(g/cm³) = 5000 kg/m³.
Therefore, 5 grams per cubic centimeter is equal to 5000 kilograms per cubic meter.

Always write down the units you are converting from and to.
Use the correct conversion factors.
Ensure the units you are converting from cancel out, leaving you with the units you are converting to.
Double-check your calculations to minimize errors.
For complex conversions, break them down into multiple steps.