1.5 SI Prefixes

Definition

SI prefixes are standard prefixes added to SI units to represent decimal multiples and submultiples of a unit. They make very large and very small measurements easier to read, write, and compare.

Instead of writing long strings of zeros, a prefix represents a specific power of ten.

For example,

1000 m = 1 km

0.001 m = 1 mm

Using prefixes makes measurements more convenient without changing the physical quantity being measured.

Why Are Prefixes Used?

Physical quantities can vary over an enormous range of values. For example, the diameter of a galaxy may be measured in trillions upon trillions of meters, while the diameter of an atom is only a fraction of a nanometer.

Writing these values entirely in SI base units would be impractical.

SI prefixes provide a simple and consistent way to express both very large and very small measurements.

Common SI Prefixes

PrefixSymbolFactor
teraT10¹²
gigaG10⁹
megaM10⁶
kilok10³
centic10⁻²
millim10⁻³
microμ10⁻⁶
nanon10⁻⁹
picop10⁻¹²
Table 1.5.1 — Common SI Prefixes. Commonly used SI prefixes, their symbols and corresponding powers of ten.

Only the most commonly used SI prefixes are shown here. The complete list of SI prefixes extends beyond those shown here, but these are sufficient for most physics applications.

Forming Prefixed Units

The name of a prefixed unit is formed by placing the prefix directly before the unit name.

Prefix + UnitRead As
kilo + meterkilometer
centi + metercentimeter
milli + metermillimeter
micro + secondmicrosecond
mega + wattmegawatt
milli + newtonmillinewton
Table 1.5.2 — Forming Prefixed Units. Examples showing how prefixes are combined with unit names.

Using Prefixes

A prefix is placed immediately before the unit symbol.

QuantityEquivalent Value
1 km1000 m
1 cm0.01 m
1 mm0.001 m
1 μs10⁻⁶ s
1 MW10⁶ W
1 mN10⁻³ N
Table 1.5.3 — Examples of Prefixed Units. Examples of prefixed units and their equivalent values.

Notice that the prefix changes the size of the unit, not the physical quantity being measured.

Example 1

Convert 5 km to meters.

5km=5×103m=5000m5\,km = 5 \times 10^{3}\,m = 5000\,m

Example 2

Convert 250 cm to meters.

250cm=250×10−2m=2.5m250\,cm = 250 \times 10^{-2}\,m = 2.5\,m

Example 3

Convert 40 μA to amperes.

40μA=40×10−6A=4.0×10−5A40\,\mu A = 40 \times 10^{-6}\,A = 4.0 \times 10^{-5}\,A

Rules for Using SI Prefixes

  • Each prefix represents a specific power of ten.
  • A unit symbol can have only one prefix.
  • Prefixes may be used with both base units and derived units.
  • A prefix changes the size of the unit but not the physical quantity.

The original unit symbol is not modified; the prefix is simply placed before it.

Examples

  • km
  • ms
  • μA
  • kN
  • MW

Key Points

  • SI prefixes represent decimal multiples and submultiples of SI units.
  • Each prefix corresponds to a specific power of ten.
  • Prefixes simplify the expression of very large and very small measurements.
  • Prefixes can be used with both base and derived SI units.
  • The prefix changes the size of the unit, not the physical quantity.
  • Using SI prefixes makes measurements easier to read, write, and compare.

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