Ratios & Proportional Relationships

Using Rates for Unit Conversion

⚖️ Ratios & Proportional Relationships
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Using Rates for Unit Conversion

Multiply by 1 in disguise — that's all unit conversion is.

A conversion factor is a fraction equal to 1, where the numerator and denominator are the same quantity in different units. Multiplying by a conversion factor changes the unit without changing the actual measurement. You can chain multiple conversion factors together.

Dimensional Analysis Method

1Write the starting measurement as a fraction
2Multiply by conversion factor(s) as fractions
3Arrange so the unwanted unit cancels (appears in both numerator and denominator)
4Multiply numerators, multiply denominators, then simplify
🏃Converting miles per hour to feet per minute
60 miles/hour × (5,280 feet/1 mile) × (1 hour/60 minutes)
= (60 × 5,280 × 1) / (1 × 1 × 60) feet/minute
= 316,800 / 60 = 5,280 feet per minute
60 mi1 hr×5280 ft1 mi×1 hr60 min=5280ftmin\frac{60 \text{ mi}}{1 \text{ hr}} \times \frac{5280 \text{ ft}}{1 \text{ mi}} \times \frac{1 \text{ hr}}{60 \text{ min}} = 5280 \frac{\text{ft}}{\text{min}}
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Remember This!

Cross out units that appear in both numerator and denominator as you go. If the remaining unit is not what you want, flip the conversion factor.

✏️ Try It!

How many seconds are in 2.5 hours? (1 hour = 60 minutes, 1 minute = 60 seconds)

Take Quiz 📝 — 25 Questions