Units of measure and conversions | Math basics

Two systems

The US uses customary units (inches, feet, pounds, gallons) in everyday life. Science, medicine and most of the world use the metric system (meters, grams, liters). You'll meet both.

US customary units

Length	Weight	Capacity
$$12$$ inches (in.) $$= 1$$ foot (ft)	$$16$$ ounces (oz) $$= 1$$ pound (lb)	$$8$$ fluid ounces $$= 1$$ cup (c)
$$3$$ feet $$= 1$$ yard (yd)	$$2{,}000$$ pounds $$= 1$$ ton (T)	$$2$$ cups $$= 1$$ pint (pt)
$$5{,}280$$ feet $$= 1$$ mile (mi)		$$2$$ pints $$= 1$$ quart (qt)
		$$4$$ quarts $$= 1$$ gallon (gal)

Converting units

For conversions with several steps, chain them: $$1$$ gallon $$= 4$$ quarts $$= 8$$ pints $$= 16$$ cups.

The metric system

Metric units go up and down by powers of ten, so converting is just moving the decimal point.

Prefix	kilo-	hecto-	deka-	base	deci-	centi-	milli-
Means	$$1{,}000$$	$$100$$	$$10$$	$$1$$	$$0.1$$	$$0.01$$	$$0.001$$
Length	km	hm	dam	m	dm	cm	mm

The same prefixes work for grams (g) and liters (L): a kilogram is $$1{,}000$$ grams, a milliliter is $$0.001$$ liter.

Rough connections between the systems: $$1$$ inch $\approx 2.54$ cm, $$1$$ mile $\approx 1.6$ km, $$1$$ kg $\approx 2.2$ lb, $$1$$ gallon $\approx 3.8$ L.

Time

$$60$$ seconds $$= 1$$ minute, $$60$$ minutes $$= 1$$ hour, $$24$$ hours $$= 1$$ day.

Practice

Quick check

How many feet are in a yard?

Quick check

How many grams are in $$0.5$$ kg?

Length	Weight	Capacity
$\(12\)$ inches (in.) $\(= 1\)$ foot (ft)	$\(16\)$ ounces (oz) $\(= 1\)$ pound (lb)	$\(8\)$ fluid ounces $\(= 1\)$ cup (c)
$\(3\)$ feet $\(= 1\)$ yard (yd)	$\(2{,}000\)$ pounds $\(= 1\)$ ton (T)	$\(2\)$ cups $\(= 1\)$ pint (pt)
$\(5{,}280\)$ feet $\(= 1\)$ mile (mi)		$\(2\)$ pints $\(= 1\)$ quart (qt)
		$\(4\)$ quarts $\(= 1\)$ gallon (gal)

Prefix	kilo-	hecto-	deka-	base	deci-	centi-	milli-
Means	$\(1{,}000\)$	$\(100\)$	$\(10\)$	$\(1\)$	$\(0.1\)$	$\(0.01\)$	$\(0.001\)$
Length	km	hm	dam	m	dm	cm	mm