Unit Conversions & The Metric System: Study Notes

Unit Conversions & The Metric System

Introduction to Unit Conversions

Unit conversions are a fundamental skill in general chemistry, allowing students to translate measurements between different units within the metric system. Understanding how to use conversion factors and metric prefixes is essential for accurate scientific calculations.

• Base Unit: The standard unit for a quantity (e.g., meter (m), gram (g), liter (L)).

• Derived Unit: Units that are multiples or fractions of the base unit, indicated by prefixes (e.g., kilogram (kg), milliliter (mL)).

• Conversion Factor: A ratio used to convert from one unit to another, based on the relationship between units.

Metric System Prefixes

The metric system uses prefixes to denote multiples or fractions of base units. Each prefix has a specific symbol and numerical value.

Common Metric Prefixes:

Example: The prefix 'kilo' (k) means 103, so 1 kilogram (kg) = 1,000 grams (g).

General Approach to Unit Conversions

To convert between units, follow these steps:

1. Identify the starting unit and the desired unit.

2. Determine the appropriate conversion factor(s).

3. Set up the calculation so that units cancel appropriately.

4. Multiply and simplify to obtain the answer in the desired unit.

Tip: Place 10# with the base unit and 1 with the different unit (prefix).

Worked Examples

Example 1: Converting Liters to Microliters

Question: How many microliters are in 1.5 liters?

• Base unit: L

• Different unit: µL

• Conversion factor: $1 \ \mu L = 10^{-6} \ L$

Setup:

$1.5 \ L \times \frac{1 \ \mu L}{10^{-6} \ L} = 1.5 \times 10^{6} \ \mu L$

Answer: $1.5 \times 10^{6} \ \mu L$

Example 2: Converting Nanometers to Centimeters

Question: How many centimeters are in 7.6 nanometers?

• Base unit: m

• Different units: nm and cm

• Plan: nm → m → cm

• Conversion factors: $1 \ nm = 10^{-9} \ m$, $1 \ cm = 10^{-2} \ m$

Setup:

$7.6 \ nm \times \frac{10^{-9} \ m}{1 \ nm} \times \frac{1 \ cm}{10^{-2} \ m} = 7.6 \times 10^{-7} \ cm$

Answer: $7.6 \times 10^{-7} \ cm$

Practice Problems

1. Convert 7.308 nL to L

2. Convert 0.0034 mm to cm

3. Convert 8.900 kg to g

4. Convert 406 cm to nm

5. Convert 9.0 L to mL

6. Convert 5.330 dm to pm

Solutions to Practice Problems

1. Convert 7.308 nL to L

• Given: 7.308 nL

• Conversion factor: $1 \ nL = 10^{-9} \ L$

• Plan: nL → L

$7.308 \ nL \times \frac{10^{-9} \ L}{1 \ nL} = 7.308 \times 10^{-9} \ L$

Answer: $7.308 \times 10^{-9} \ L$

2. Convert 0.0034 mm to cm

• Given: 0.0034 mm

• Conversion factors: $1 \ mm = 10^{-3} \ m$, $1 \ cm = 10^{-2} \ m$

• Plan: mm → m → cm

$0.0034 \ mm \times \frac{10^{-3} \ m}{1 \ mm} \times \frac{1 \ cm}{10^{-2} \ m} = 3.4 \times 10^{-4} \ cm$

Answer: $3.4 \times 10^{-4} \ cm$

3. Convert 8.900 kg to g

• Given: 8.900 kg

• Conversion factor: $1 \ kg = 10^{3} \ g$

• Plan: kg → g

$8.900 \ kg \times \frac{10^{3} \ g}{1 \ kg} = 8.900 \times 10^{3} \ g$

Answer: $8.900 \times 10^{3} \ g$

4. Convert 406 cm to nm

• Given: 406 cm

• Conversion factors: $1 \ cm = 10^{-2} \ m$, $1 \ nm = 10^{-9} \ m$

• Plan: cm → m → nm

$406 \ cm \times \frac{10^{-2} \ m}{1 \ cm} \times \frac{1 \ nm}{10^{-9} \ m} = 4.06 \times 10^{9} \ nm$

Answer: $4.06 \times 10^{9} \ nm$

5. Convert 9.0 L to mL

• Given: 9.0 L

• Conversion factor: $1 \ mL = 10^{-3} \ L$

• Plan: L → mL

$9.0 \ L \times \frac{1 \ mL}{10^{-3} \ L} = 9.0 \times 10^{3} \ mL$

Answer: $9.0 \times 10^{3} \ mL$

6. Convert 5.330 dm to pm

• Given: 5.330 dm

• Conversion factors: $1 \ dm = 10^{-1} \ m$, $1 \ pm = 10^{-12} \ m$

• Plan: dm → m → pm

$5.330 \ dm \times \frac{10^{-1} \ m}{1 \ dm} \times \frac{1 \ pm}{10^{-12} \ m} = 5.330 \times 10^{11} \ pm$

Answer: $5.330 \times 10^{11} \ pm$

Summary Table: Metric Prefixes

The following table summarizes the most common metric prefixes, their symbols, and their numerical values:

Name	Symbol	Number
Tera	T	$10^{12}$
Giga	G	$10^{9}$
Mega	M	$10^{6}$
Kilo	k	$10^{3}$
Hecto	h	$10^{2}$
Deka	da	$10^{1}$
Deci	d	$10^{-1}$
Centi	c	$10^{-2}$
Milli	m	$10^{-3}$
Micro	\mu	$10^{-6}$
Nano	n	$10^{-9}$
Pico	p	$10^{-12}$
Femto	f	$10^{-15}$

Application: Use this table to quickly identify conversion factors for unit conversions in chemistry.