Metric Prefixes and Unit Conversions in Chemistry

Measurement and Problem Solving

Metric Prefixes

Metric prefixes are essential modifiers in chemistry that indicate multiples or fractions of base units. They help express very large or very small quantities in a manageable form.

• Definition: Metric prefixes are symbols or words placed in front of base units to indicate a specific power of ten multiplier.

• Examples of Base Units: meter (m), gram (g), liter (L), second (s)

Common Metric Prefix Multipliers

Prefix	Symbol	Multiplier	Power of Ten
tera	T	1,000,000,000,000	$10^{12}$
giga	G	1,000,000,000	$10^{9}$
mega	M	1,000,000	$10^{6}$
kilo	k	1,000	$10^{3}$
hecto	h	100	$10^{2}$
deca	da	10	$10^{1}$
base unit	-	1	$10^{0}$
deci	d	0.1	$10^{-1}$
centi	c	0.01	$10^{-2}$
milli	m	0.001	$10^{-3}$
micro	μ	0.000001	$10^{-6}$
nano	n	0.000000001	$10^{-9}$
pico	p	0.000000000001	$10^{-12}$

Memory Tool: The phrase "The Great Monarch King Henry's Daughter Barbara drinks chocolate milk until nine pm" can help remember the order of prefixes from largest to smallest.

Using Metric Prefixes

• Metric prefixes act as "labels" that can be placed in front of various base units to indicate the scale of measurement.

• For example, 1 kilometer (km) = $10^3$ meters (m).

Table: Prefix Placement

Prefix	Base Unit	Example
kilo-	meter	kilometer (km)
milli-	gram	milligram (mg)
micro-	liter	microliter (μL)

Unit Conversion Steps

1. If the given value has a metric prefix, first convert it to the base unit.

2. After converting to the base unit, convert to the new metric prefix if needed.

3. Always place the coefficient (number) on one side and the metric prefix on the other.

Example: Convert 654 mg to g.

Step 1: $654 \text{ mg} = 654 \times 10^{-3} \text{ g} = 0.654 \text{ g}$

Practice Problems

• Which quantity is smaller? 155 pm or $7.8 \times 10^{-8}$ cm? $7.8 \times 10^{-8}$ cm is smaller.

• Express using prefix multipliers (no exponents):

  • 12 x $10^{-3}$ L = 12 mL

  • 87 x $10^{-6}$ g = 87 μg

  • 1.5 x $10^{3}$ g = 1.5 kg

• Express in scientific notation with only the base unit:

  • 81 cm = $8.1 \times 10^{-1}$ m

  • 15 mg = $1.5 \times 10^{-2}$ g

  • 2.7 mm = $2.7 \times 10^{-3}$ m

• Volume conversion: If a room has a volume of $1.5 \times 10^{9}$ cm$^3$, what is the volume in km$^3$? $1.5 \times 10^{-12}$ km$^3$

Additional info: Understanding metric prefixes and unit conversions is foundational for all measurements in chemistry, ensuring accuracy and consistency in scientific communication.