Understanding and working with units is essential in everyday life, science, engineering, and many professions. Measurements let us describe and compare objects, distances, time intervals, volumes, weights, and much more. This section introduces the U.S. customary system and the metric system, shows how to convert units within and between these systems, and demonstrates how units help you solve real-world problems.

Why do we have different measurement systems?

Measurement systems developed for historical and practical reasons.

The U.S. customary system grew out of older British measurement traditions. Many early units were tied to everyday human experiences, such as the length of a foot. Over time, these units became standardized and are still commonly used in the United States for construction, travel distances, and daily life.

The metric system was designed later with consistency and scientific use in mind. Because it is based on powers of $10$, it scales smoothly between very large and very small quantities. That makes it especially useful in science, engineering, medicine, and international communication. Today, most countries use the metric system, while the United States primarily uses the U.S. customary system (with metric units used often in technical fields).

Because both systems are in use, conversions are necessary whenever measurements move between industries, countries, or contexts. Knowing how to work in both systems helps you interpret information accurately and communicate measurements clearly.

U.S. customary system

The U.S. customary system is mainly used in the United States. It includes units for length, volume, weight, and time. Because it is not based on powers of $10$, conversions depend on specific conversion relationships.

Length units

Unit	Abbreviation
inch	in
foot	ft
yard	yd
mile	mi

Length relationships

Original	Converted
$12$ inches	$1$ foot
$3$ feet	$1$ yard
$5280$ feet	$1$ mile

Volume units

Unit	Abbreviation
cup	c
pint	pt
quart	qt
gallon	gal

Volume relationships

Original	Converted
$2$ cups	$1$ pint
$2$ pints	$1$ quart
$4$ quarts	$1$ gallon

Weight units

Unit	Abbreviation
ounce	oz
pound	lb
ton	ton

Weight relationships

Original	Converted
$16$ ounces	$1$ pound
$2000$ pounds	$1$ ton

Time units

Unit	Abbreviation
second	s
minute	min
hour	hr

Time relationships

Original	Converted
$60$ seconds	$1$ minute
$60$ minutes	$1$ hour

Metric system

The metric system is used worldwide and is based on powers of ten. Prefixes tell you how many powers of $10$ separate a unit from the base unit. This structure makes conversions predictable and helps reduce calculation errors.

You’ll see metric units often in science experiments, medical dosing, engineering design, and international data reporting. Because the system scales in a consistent way, it’s well suited for precision and for comparing measurements across different fields.

Base units

Quantity	Base unit	Abbreviation
Length	meter	m
Volume	liter	L
Mass	gram	g
Time	second	s

Common metric prefixes

Prefix	Symbol	Multiplier
kilo	k	$10^3$
hecto	h	$10^2$
deka	da	$10^1$
(none)	-	$10^0$
deci	d	$10^{-1}$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	µ	$10^{-6}$
nano	n	$10^{-9}$
pico	p	$10^{-12}$

Metric prefixes and conversions

In everyday situations - like reading medicine labels, interpreting scientific data, or converting distances on a map - you often need to convert between metric units. Because the metric system is based on powers of $10$, these conversions follow consistent patterns.

Example: Convert $5$ kilometers to meters You might do this when interpreting a road race distance or a map scale.

(spoiler)

• $1\mathrm{km}=10^3\mathrm{m}$, so
• $5\mathrm{km}=5\times 10^3=5000\mathrm{m}$

Answer: $5000\mathrm{m}$

Example: Convert $0.03$ liters to milliliters This type of conversion is common when measuring beverages or laboratory liquids.

(spoiler)

• $1\mathrm{L}=10^3\mathrm{mL}$, so
• $0.03\mathrm{L}=0.03\times 10^3=30\mathrm{mL}$

Answer: $30\mathrm{mL}$

Example: Medicine dosage Medication instructions are often written using very small metric units. A doctor prescribes $250$ µg of a medication. How many milligrams is that?

(spoiler)

• $1\mathrm{mg}=1000\mu \mathrm{g}$, so
• $250÷1000=0.25$

Answer: $0.25\mathrm{mg}$

U.S. customary to metric conversion factors

Multiply by	Old equals new
$2.54$	$1$ in = $2.54$ cm
$0.3048$	$1$ ft = $0.3048$ m
$1.609$	$1$ mi = $1.609$ km
$0.4536$	$1$ lb = $0.4536$ kg
$3.785$	$1$ gal = $3.785$ L

Converting between systems

Converting between U.S. customary and metric units comes up often in travel, international communication, and scientific work. A reliable approach is to start with a known conversion factor and set up the calculation so the unwanted unit cancels.

Example: Convert $10$ miles to kilometers A fitness tracker or GPS device may report distances in kilometers.

(spoiler)

• $1$ mile $\approx 1.609$ km, so
• $10\times 1.609=16.09$

Answer: $16.09$ km

Example: Convert $2$ liters to gallons This is useful when comparing beverage sizes sold in different countries.

(spoiler)

• $1$ gallon $\approx 3.785$ L, so
• $2÷3.785\approx 0.529$

Answer: $0.529$ gallons

Applying units in real life

Units turn numbers into usable information for planning, estimating, and decision-making. Including units as you calculate also helps you check that your result makes sense.

Example: Road trip fuel estimate You plan to drive $250$ miles (mi). Your car’s fuel efficiency is $30$ miles per gallon (mi/gal). How many gallons of gas will you need?

• Set up the ratio so miles cancel:

$$>\frac{250\text{mi}}{30\text{mi/gal}}$$

• Compute the value:

$$>\frac{250}{30}\approx 8.33$$

Answer: You will need approximately $8.33$ gallons of gas.

Example: Paint coverage A can of paint covers $350$ square feet. How many cans are needed to paint a wall with an area of $1120$ square feet?

(spoiler)

• Divide total area by coverage per can:

$$>\frac{1120{\text{ft}}^2}{350{\text{ft}}^2/\text{can}}=3.2$$

• Since you cannot buy a fraction of a can, round up.

Answer: $4$ cans of paint are needed.