47.2: Introduction

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The system of units used in the physical sciences is based on the metric system. Numbers that describe physical quantities range from the very large to the very small, so a set of standard prefixes are used to designate convenient-sized units that differ by multiples of ten. Every step in the metric system is a multiple of 10.

Table \(\PageIndex{1}\): Prefixes to designate convenient-sized units that differ by multiples of ten
Multiple	Prefix	Symbol
\(10^{24}\)	yotta	Y
\(10^{21}\)	zetta	Z
\(10^{18}\)	exa	E
\(10^{15}\)	peta	P
\(10^{12}\)	tera	T
\(10^{9}\)	giga	G
\(10^{6}\)	mega	M
\(10^{3}\)	kilo	k
\(10^{1}\)	deca	da
\(10^0\)
\(10^{-1}\)	deci	d
\(10^{-2}\)	centi	c
\(10^{-3}\)	milli	m
\(10^{-6}\)	micro	μ
\(10^{-9}\)	nano	n
\(10^{-12}\)	pico	p
\(10^{-15}\)	femto	f
\(10^{-18}\)	atto	a
\(10^{-21}\)	zepto	z
\(10^{-24}\)	yocto	y

The United States continues to use English units. Conversion factors utilize equivalent sized measurements, to change from one unit to another. For example, 1 inch and 2.54 centimeters measure the exact same length. Converting from one unit to another requires multiplying by the appropriate conversion factor.

Table \(\PageIndex{2}\): English to Metric conversion
English to Metric
1 inch = 2.54 centimeter
1 mile = 1609 meters
0.2248 lb = 1 Newton

Example: [Measurement] x [Conversion Factor] = New Number

\[12 \cancel{\text { inches }} \times \dfrac {2.54 \text { centimeters}}{1 \cancel {\text { inch}}} = 30.48 \text { centimeters} \nonumber \]

The inches in the numerator and the inches in the denominator cancel

Contributors and Attributions

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