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Unit Conversions

Convert between units of measurement, including metric, imperial, and mixed systems.

Before you read
Answer first — see what you already know.

A commercial aquarium holds 12,000 gallons of saltwater. If 1 gallon liters, approximately how many liters does the aquarium hold?

Check your answer
Answer:

C

Before you read
Answer first — see what you already know.

A marathon runner finishes a 10-kilometer charity race in 48 minutes. What is the runner's average speed in miles per hour? (1 mile 1.609 km)

Check your answer
Answer:

B

Theory

The Conversion Factor Method

To convert units, multiply by a conversion factor — a fraction equal to 1:
Original×desired unitoriginal unit=Converted\text{Original} \times \frac{\text{desired unit}}{\text{original unit}} = \text{Converted}

Example: Convert 5 feet to inches.
5 ft×12 in1 ft=60 in5 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 60 \text{ in}

The key: the old unit cancels out, and you're left with the new unit.

  1. 5 km5 \text{ km}
  2. 5×1000 m5 \times 1000 \text{ m}1 km = 1000 m
  3. 5000 m5000 \text{ m}
Converting kilometers to meters
Example 1

Convert 90 kilometers per hour to meters per second.

90kmhr×1000 m1 km×1 hr3600 s90 \frac{\text{km}}{\text{hr}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{3600 \text{ s}}

=90×10003600=900003600=25 m/s= \frac{90 \times 1000}{3600} = \frac{90000}{3600} = 25 \text{ m/s}

25 m/s
Example 2

A car uses 8 liters of fuel per 100 km. If gas costs $1.50 per liter, what is the fuel cost for a 350 km trip?

Fuel needed: 8100×350=28\frac{8}{100} \times 350 = 28 liters

Cost: 28×1.50=$42.0028 \times 1.50 = \$42.00

$42.00
Theory

Key Conversions to Know

The SAT provides a reference sheet, but knowing these speeds things up:

Length: 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5,280 ft, 1 km = 1,000 m, 1 in ≈\approx 2.54 cm

Volume: 1 gal = 4 qt, 1 L = 1,000 mL

Weight: 1 lb = 16 oz, 1 kg ≈\approx 2.2 lb

Time: 1 hr = 60 min = 3,600 s

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