Lesson 1 of 6 · Ratios, conversions & dimensional checks
Make the units do useful work
8 minute lesson · 3 checks along the way
Your goal for this lessonCompare like quantities, convert compound units, and use dimensional checks to catch a plausible-looking error.
Follow a linked name to explore its archive card. “Back to your lesson” brings you to the same part of the reading.
Words with a dotted underline open a short definition right here in the lesson.
Compare quantities before comparing numbers
A rover route and its safety margin might arrive in different units. Dividing 0.72 kilometers by 180 meters does not mean dividing 0.72 by 180 and stopping. Express the route as 720 meters first: 720 m ÷ 180 m = 4. The route is four times the comparison length. Matching units cancel in this , leaving a number with a clear meaning.
A ratio can also connect different kinds of quantity. Distance divided by elapsed time gives a speed with units such as meters per second. Those units do not cancel completely, and that is useful: they tell you what the answer measures. Before calculating, name the numerator, denominator, and desired output. A bare number cannot tell a flight team whether you mean a length, a time, or a rate.
Check 1 of 3
10 pointsUse the reading above. You can try again without losing points.
Convert a complete rate
Use a fictional training rover that travels a path of 72 meters in six minutes. Its average speed over the whole interval is 72 ÷ 6 = 12 meters per minute. To express the same rate in meters per second, multiply by one minute per 60 seconds. The minute units cancel, giving 12/60 = 0.20 m/s. Including a pause would lower this whole-interval average without changing the wheel speed during motion.
For kilometers per hour, multiply 12 m/min by 60 min/h and divide by 1,000 m/km: the answer is 0.72 km/h. The numerical values 12, 0.20, and 0.72 describe the same average speed in different units. A conversion changes representation, not rover performance. Keep both conversion factors visible until the remaining units match the quantity requested.
Compare the evidence
Audit the units on a submitted result
Both cards use the same invented area. The linked source explains the mathematical method; it does not supply a spacecraft measurement.
Single-factor conversion
- When and where
- Original fictional practice example · Training calculation; not mission telemetry
- Purpose
- Review a proposed area conversion.
- What it supports
- Submitted: 400 cm² ÷ 100 = 4 m².
- What remains uncertain
- The calculation applies a length conversion only once and therefore does not preserve area.
Two-dimensional conversion
- When and where
- Original fictional practice example · Training calculation; not mission telemetry
- Purpose
- Track both length factors.
- What it supports
- Checked: 400 cm² × (0.01 m/cm)² = 0.040 m².
- What remains uncertain
- Correct conversion preserves the supplied value’s precision; it does not verify how the area was measured.
Why does the exponent on the unit affect the conversion factor?
Compare your reasoning
A square centimeter is a product of two centimeter lengths. Each length becomes 0.01 meter, so the combined factor is 0.0001. The example separates an arithmetic correction from an independent check of the original measurement.
Check 2 of 3
10 pointsUse the reading above. You can try again without losing points.
Work through a decision
Catch the squared-unit trap
A hypothetical instrument panel covers 400 square centimeters. Since one centimeter is 0.01 meter, one square centimeter is 0.01 m × 0.01 m = 0.0001 square meter. Therefore 400 cm² = 0.040 m². Dividing by only 100 would produce the wrong area. The length conversion must be applied twice because area combines two lengths; a volume conversion would apply it three times.
Now review a planning sheet that predicts travel time by multiplying distance by speed. Its units become m²/s, not seconds, revealing a problem before you examine the numbers. Dividing distance by speed gives m ÷ (m/s) = s. A unit check can reject many wrong equations, but it cannot prove an equation physically correct: multiplying the correct time by two would still leave seconds.
Check 3 of 3
10 pointsUse the reading above. You can try again without losing points.
Attach the assumptions to the answer
NASA identifies a failure to translate English units to metric in navigation as a cause of the loss of Mars Climate Orbiter in 1999. The lesson is broader than memorizing conversion factors. Quantities passed between people or systems need an agreed meaning, unit, and check. Our rover arithmetic is an invented exercise, not a reconstruction of that mission’s navigation problem or its organizational investigation.
The Sojourner rover and Mars Pathfinder lander archive photograph shows hardware, airbags, and a deployment ramp. It does not supply the fictional rover’s path length or elapsed time. Use the stated exercise inputs for those calculations. Finish with an estimate of whether the answer is reasonable, and preserve any measurement uncertainty. Exact unit definitions cannot turn a rounded observation into a more precise one simply by adding zeros.
NASA’s PIA00614 view shows part of Sojourner, its rolled rear ramp, and Pathfinder’s airbags. Visible panel boundaries remain in this preserved released image. This is hardware and deployment context, not a timed record of the fictional 72-meter practice drive.
Look closely
What information would be missing if someone tried to obtain the lesson’s average speed just from this picture?
See what to notice
A single hardware view does not provide the traveled path or elapsed interval. Those are supplied explicitly in the fictional exercise. Displayed dimensions also require camera geometry and a physical scale before becoming measured lengths.
Put it together
Your lesson progress
Each check connects to a part of the story. Complete all 3 to earn your 25-point lesson bonus.
Go to the source
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