Unit-conversion recall sprint

Recall standard conversions (length, weight, capacity, time, metric prefixes).

A fluency sprint: build the speed and accuracy you need to do this calculation instantly on test day.

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What to memorize: unit conversions

Customary units

Metric: 10 mm = 1 cm; 100 cm = 1 m; 1,000 m = 1 km; 1,000 g = 1 kg; 1,000 kg = 1 metric ton; 1,000 mL = 1 L.

Time: 60 seconds = 1 minute; 60 minutes = 1 hour; 24 hours = 1 day.

To a bigger unit, divide. To a smaller unit, multiply. 180 inches \(\div 12 = 15\) feet, then \(15 \div 3 = 5\) yards.

Square units use the factor twice: 1 square yard = \(3 \times 3 = 9\) square feet.

Common slips: multiplying when you must divide, and stopping after the first step of a two-step conversion.

Worked examples

Example 1.
How many ounces are in 4 pounds? (1 pound = 16 ounces)
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Answer:
B

\(4 \times 16 = 64\) ounces. (Dividing, \(4 \div 16\), gives 0.25. Not converting leaves 4. Adding, \(4 + 16\), gives 20.)

Example 2.
Given that 1 centimeter = 10 millimeters and 1 meter = 100 centimeters, how many meters are in 8000 millimeters?
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Answer:
A

Convert in two steps: \(8000 \div 10 = 800\) centimeters, then \(800 \div 100 = 8\) meters. (Stopping after the first step leaves 800 centimeters. Multiplying by 100 in the second step gives 80000. Dividing 8000 by 100 only once gives 80.)

Example 3.
On a map, 1 inch represents 6 feet. A park covers 23 square inches on the map. What is the actual area of the park, in square yards?
Show answer and explanation
Answer:
B

One inch is 6 feet, which is \(6 \div 3 = 2\) yards. A square inch on the map is \(2 \times 2 = 4\) square yards, so the park is \(23 \times 4 = 92\) square yards. (Multiplying by 2 only once gives 46: area uses the scale twice. Stopping at square feet, \(23 \times 6 \times 6\), gives 828. Dividing the square feet by 3 instead of 9 gives 276.)