Dimensional Analysis, Unit Conversions, and Metric Prefixes — Vocabulary

Vocabulary flashcards covering key terms from the lecture on converting units, planning dimensional analysis, metric prefixes, area/volume conversions, and checking for correctness.

Dimensional analysis

A method for converting units by multiplying by conversion factors to cancel out undesired units and obtain the desired ones.

Conversion factor

A ratio that equals 1 and relates two units (e.g., 1 mile / 5280 feet); used to convert between units.

Unit cancellation

Arranging units in fractions so that the units cancel each other, leaving the target unit.

Base unit (metric)

A fundamental unit in the metric system used as a stepping stone in conversions, e.g., meter (length), gram (mass), second (time).

Plan arrow (dimensional analysis)

A conceptual plan showing the sequence of conversions; guides which units to cancel first.

Two-step conversion

A conversion that requires two or more sequential conversions to reach the final units (e.g., pm -> m -> cm).

Common conversion factors

Well-known relationships used in problems, e.g., 1 mile = 5280 feet; 1 hour = 60 minutes = 3600 seconds; 1 cm = 0.01 m.

Significant figures

Digits that carry measurement precision; the decimal point can affect which zeros are significant; exact conversion factors do not limit significant figures.

Plan-your-calculation practice

A recommendation to write out steps and include units to avoid mistakes, especially when problems have multiple steps.

Miles per hour to feet per second

60 mph ≈ 88 ft/s; 1 mph ≈ 1.4667 ft/s.

Area units and squaring

When converting area, square both the numerical factors and the units (e.g., cm^2 to m^2 uses (0.01 m)^2 = 1e-4 m^2 per cm^2).

1 inch to centimeters

1 inch = 2.54 centimeters (2.54 cm per inch); used in area conversions by squaring.

1 cm = 0.01 m

Length conversion between centimeters and meters; 1 cm is 0.01 m.

1 cm^2 = 1e-4 m^2

Area conversion derived by squaring 1 cm = 0.01 m.

Density

Mass per unit volume; e.g., cardboard density ~0.69 g/cm^3; used to check magnitudes (e.g., cardboard floats in water).

Mass to volume conversion example

Using a density like 43 lb/ft^3 and converting to g/cm^3 involves converting pounds to grams and cubic feet to cubic centimeters.

Cubed conversion factors

For volume, cube the conversion factors and units (e.g., 1 ft = 12 in; cube to convert ft^3 to in^3; then convert to cm^3 with 2.54 cm per inch).

Scientific notation in conversions

Use scientific notation to express numbers; preserve significant figures and avoid rounding at intermediate steps.

Error checking and magnitudes

Check that the final magnitude makes sense in real-world terms (e.g., tiny areas yield small densities or costs).