Unit Conversion: Foundations
[Video Placeholder - Introduction to unit conversion]
Duration: 5:45
Understanding Unit Conversion
Unit conversion involves changing a measurement from one unit to another while maintaining the same quantity. We use conversion factors that express the relationship between units.
1 foot = 12 inches → Conversion factor: 12 in/1 ft or 1 ft/12 in
Dimensional Analysis Method
Write the given measurement as a fraction
Multiply by conversion factor(s) as fractions
Arrange so unwanted units cancel out
Multiply numerators and denominators
Simplify the result
Example 1: Simple Conversion
Convert 5 feet to inches.
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Step 1: Write as fraction: 5 ft/1
Step 2: Multiply by conversion factor: (5 ft/1) × (12 in/1 ft)
Note: ft in numerator and denominator cancel out
Step 3: Multiply: (5 × 12 in) / (1 × 1) = 60 in
Answer: 5 feet = 60 inches
Multi-Step Conversions
Example 2: Compound Conversion
Convert 2 hours to seconds.
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Step 1: Hours to minutes: (2 hr/1) × (60 min/1 hr) = 120 min
Step 2: Minutes to seconds: (120 min/1) × (60 sec/1 min) = 7,200 sec
Or combined: (2 hr/1) × (60 min/1 hr) × (60 sec/1 min)
Answer: 2 hours = 7,200 seconds
Metric System Conversions
The metric system uses powers of 10. Common prefixes:
Prefix
Meaning
Factor
kilo-
thousand
10³
centi-
hundredth
10⁻²
milli-
thousandth
10⁻³
Example 3: Metric Conversion
Convert 450 centimeters to meters.
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Step 1: Know that 100 cm = 1 m
Step 2: Set up conversion: (450 cm/1) × (1 m/100 cm)
cm units cancel out
Step 3: Calculate: 450/100 = 4.5 m
Answer: 450 cm = 4.5 m
SAT-Style Problems
Example 4: Rate Conversion
A car travels 60 miles per hour. What is its speed in feet per second?
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Step 1: Convert miles to feet: (60 mi/1 hr) × (5280 ft/1 mi) = 316,800 ft/hr
Step 2: Convert hours to seconds: (316,800 ft/1 hr) × (1 hr/3600 sec) = 88 ft/sec
Or combined: (60 mi/hr) × (5280 ft/mi) × (1 hr/3600 sec)
Answer: 88 feet per second