Unit Conversion Problems (Intermediate)

These problems will help you practice multi-step unit conversions, often involving converting between different measurement systems or multiple time units.

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Example Problem: Kilometers per Hour to Meters per Second

Problem: A car is traveling at a speed of 90 kilometers per hour (km/h). Convert this speed to meters per second (m/s).

Step 1: What you have, what you want.

You have 90 km/h. You want meters per second (m/s).

Step 2: Find your helper numbers (conversion factors).

You'll need to convert kilometers to meters, and hours to seconds. Here are the factors:

• 1 kilometer (km) = 1000 meters (m)
• 1 hour (h) = 60 minutes (min)
• 1 minute (min) = 60 seconds (s)

Step 3: Set it up.

Arrange your starting value and helper numbers. Make sure the units you want to get rid of are on the bottom, and the new units are on the top. This makes the old units "cancel out."

$$ 90 \frac{\text{km}}{\text{h}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ s}} $$

Notice how 'km', 'h', and 'min' will cancel out, leaving 'm' on top and 's' on bottom.

Step 4: Do the math.

Multiply all the numbers on the top. Then, divide by all the numbers on the bottom. Your answer should have the new units (m/s).

$$ 90 \times \frac{1000}{60 \times 60} \frac{\text{m}}{\text{s}} = 90 \times \frac{1000}{3600} \frac{\text{m}}{\text{s}} = 25 \frac{\text{m}}{\text{s}} $$

Answer: 25 m/s

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Common Conversion Factors

Here are some common conversion factors you might need for these problems:

• 1 mile = 1.609 kilometers (km)
• 1 foot (ft) = 0.3048 meters (m)
• 1 kilogram (kg) = 2.205 pounds (lbs)
• 1 kilometer (km) = 1000 meters (m)
• 1 meter (m) = 100 centimeters (cm)
• 1 inch (in) = 2.54 centimeters (cm)
• 1 second (s) = 1000 milliseconds (ms)
• 1 minute (min) = 60 seconds (s)
• 1 hour (hr) = 60 minutes (min)
• 1 day = 24 hours (hr)

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Practice Problems

Solve these problems. Check your answers using the Answer Key at the bottom of the page.

Problem 1: Miles per Hour to Meters per Second

A car’s speed limit sign shows 65 miles per hour (mph). What is this speed in meters per second (m/s)?

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Problem 2: Feet per Second to Kilometers per Hour

An athlete runs at a speed of 20 feet per second (ft/s). Convert this speed to kilometers per hour (km/h).

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Problem 3: Days to Seconds

How many seconds (s) are there in 3 days?

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Problem 4: Pounds to Grams

A physics textbook has a mass of 4.8 pounds (lbs). What is its mass in grams (g)?

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Problem 5: Kilometers per Minute to Meters per Second

A high-speed train travels at 2.5 kilometers per minute (km/min). What is its speed in meters per second (m/s)?

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Show Answer Key

Problem 1: Approximately 29.06 m/s

Problem 2: Approximately 21.95 km/h

Problem 3: 259,200 s

Problem 4: Approximately 2176.8 g

Problem 5: Approximately 41.67 m/s

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Related Concepts & Skills

• Unit Conversions (Skill)
• Dimensional Analysis (Concept)