Metric Prefixes and Unit Conversions in GOB Chemistry

Metric Prefixes and Unit Conversions

Introduction to Metric Prefixes

Metric prefixes are modifiers that represent specific powers of ten and are used to express very large or very small quantities in the metric system. They are essential for scientific measurements and calculations in chemistry.

• Metric Prefixes are attached to base units (such as meter, gram, liter) to indicate multiples or fractions of these units.

• Each prefix corresponds to a specific power of ten.

Common Metric Prefixes

The following table summarizes the most commonly used metric prefixes, their symbols, and their corresponding powers of ten:

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	-	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	$10^{-12}$

Mnemonic for Metric Prefixes

To remember the order of metric prefixes, use the following mnemonic:

• The Great Monarch King Henry's Daughter Barbara drinks chocolate milk until nine pm

• This corresponds to: tera, giga, mega, kilo, hecto, deca, BASE, deci, centi, milli, micro, nano, pico.

Metric Prefixes as Labels

Metric prefixes can be placed in front of various base units to indicate different magnitudes. For example:

Base Units	Metric Prefixes
L (liter)	mL, μL
g (gram)	mg, kg
mol (mole)	mmol

Unit Conversion Using Metric Prefixes

Converting between units with different metric prefixes involves the following steps:

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

2. To cancel out units, ensure they are on opposite levels (numerator/denominator).

3. Always place the coefficient '1' on the side with the metric prefix.

4. If necessary, convert the base unit to a new metric prefix.

Example Conversion

Example: Convert 694 kg to μg.

• Step 1: Convert kilograms to grams: $694\ \text{kg} \times \frac{10^3\ \text{g}}{1\ \text{kg}} = 694,000\ \text{g}$

• Step 2: Convert grams to micrograms: $694,000\ \text{g} \times \frac{10^6\ \mu\text{g}}{1\ \text{g}} = 6.94 \times 10^{11}\ \mu\text{g}$

Practice Problems and Solutions

• Which quantity is smaller? 155 pm or $7.8 \times 10^{-9}$ cm Solution: $7.8 \times 10^{-9}$ cm = 0.078 pm, so 69 pm is smaller.

• Express with prefix multipliers (no exponents):

  • 32 x $10^{12}$ L = 3.2 pL

  • 7.3 x $10^{-3}$ g = 7.3 mg

  • 18.5 x $10^{11}$ s = 1.85 Ts

• Express in scientific notation with only the base unit:

  • 83 μm = $8.3 \times 10^{-5}$ m

  • 193 kg = $1.93 \times 10^{2}$ kg

  • 2.7 mmol = $2.7 \times 10^{-3}$ mol

• Volume conversion: If a room has a volume of $1.15 \times 10^4$ cm³, what is the volume in km³? Solution: $1.15 \times 10^4$ cm³ = $1.242 \times 10^{-8}$ km³

Key Points to Remember

• Metric prefixes simplify the expression of very large or very small numbers.

• Always use the correct conversion factor when switching between units with different prefixes.

• Scientific notation is useful for expressing quantities in base units without prefixes.