The Metric System

Base Units and Derived Units

Metric System

A decimal-based system of measurement used worldwide in science; based on powers of 10.

Base Units

The standard units in the metric system: meter (length), gram (mass), liter (volume), second (time), Kelvin (temperature), mole (amount of substance), ampere (electric current).

Length Unit

Meter (m) is the base unit of length.

Mass Unit

Gram (g) is the basic unit of mass; kilogram (kg) is the SI base unit.

Volume Unit

Liter (L) is commonly used for liquid volume; 1 L = 1,000 mL = 1 dm³.

Time Unit

Second (s) is the SI unit of time.

Temperature Unit

Kelvin (K) is the SI unit; Celsius (°C) is also commonly used (K = °C + 273.15).

Common Metric Prefixes

kilo- (10³), hecto- (10²), deka- (10¹), deci- (10⁻¹), centi- (10⁻²), milli- (10⁻³), micro- (10⁻⁶), nano- (10⁻⁹)

kilo- (k)

1,000 times the base unit (10³)

hecto- (h)

100 times the base unit (10²)

deka- (da)

10 times the base unit (10¹)

base unit

1 (10⁰)

deci- (d)

0.1 times the base unit (10⁻¹)

centi- (c)

0.01 times the base unit (10⁻²)

milli- (m)

0.001 times the base unit (10⁻³)

micro- (µ)

0.000001 times the base unit (10⁻⁶)

nano- (n)

0.000000001 times the base unit (10⁻⁹)

Converting Metric Units

Move the decimal point left or right based on prefix change; each step is a factor of 10.

Mnemonic for Metric Prefixes

"Kangaroos Hop Down Big Ditches Chasing Mice" (kilo-, hecto-, deka-, base, deci-, centi-, milli-)

Scientific Notation

A method to express very large or very small numbers using powers of 10 (e.g., 6.02 × 10²³).

Why Metric System is Used

It's universal, consistent, easy to convert, and based on the decimal system.

Derived Units

Units formed by combining base units (e.g., speed = meters/second, density = kg/m³).

Area

The amount of surface; SI unit is square meters (m²).

Volume

The amount of space occupied; SI unit is cubic meters (m³), often measured in liters (1 m³ = 1,000 L).

Density

Mass per unit volume; SI unit is kg/m³, commonly g/cm³ or g/mL in chemistry.

Speed

Distance per unit time; SI unit is meters per second (m/s).

Acceleration

Change in velocity over time; SI unit is meters per second squared (m/s²).

Force

Measure of push or pull; SI unit is the newton (N), where 1 N = 1 kg·m/s².

Pressure

Force per unit area; SI unit is the pascal (Pa), where 1 Pa = 1 N/m².

Energy or Work

Ability to do work; SI unit is the joule (J), where 1 J = 1 N·m.

Power

Rate of doing work; SI unit is the watt (W), where 1 W = 1 J/s.

Temperature Conversions

K = °C + 273.15; °C = K - 273.15.

Volume Conversions

1 L = 1,000 mL; 1 m³ = 1,000 L; 1 cm³ = 1 mL.

Mass Conversions

1 kg = 1,000 g; 1 g = 1,000 mg.

Length Conversions

1 m = 100 cm; 1 m = 1,000 mm; 1 km = 1,000 m.

Time Conversions

1 minute = 60 seconds; 1 hour = 3,600 seconds.

Dimensional Analysis

A method of converting between units using conversion factors and unit cancellation.

Conversion Factor

A ratio that expresses how many of one unit equals another (e.g., 1 kg / 1,000 g).

Tips for Metric Conversions

1) Write down the given unit. 2) Multiply by conversion factors. 3) Cancel units. 4) Solve.

Multi-Step Conversions

When converting across more than one prefix or dimension, use sequential conversion factors.

Density Formula

Density = mass ÷ volume; rearrange to find mass or volume if needed.

Common Density Units

g/mL or g/cm³ for liquids and solids; kg/m³ for gases.