MET 18200 - Significant Figures and Unit Conversions

Flashcards covering key vocabulary related to significant figures, their rules in measurement and computation, and unit conversions including fundamental dimensions, systems, prefixes, conversion methods, and temperature conversions.

Why care about significant figures?

The numerical value of every observed measurement is an approximation, unlike analytically derived numbers which are exact or truncated.

Significant Figures

Each of the digits in a number that are used to express it to the required degree of accuracy.

Non-zero digits (in significant figures)

Are always significant.

Zeros located between non-zero digits (in significant figures)

Are always significant.

Trailing zeros (in significant figures)

Only significant if a decimal point is present.

Rules for Counting Significant Digits: Non-zero and in-between zeros

All non-zero digits and any zeros contained between non-zero digits count.

Rules for Counting Significant Digits: Leading zeros

Leading zeros don't count.

Rules for Counting Significant Digits: Trailing zeros with decimal

Trailing zeros count if there is a decimal point.

Rules for Counting Significant Digits: Trailing zeros without decimal

May or may not count; the most conservative answer (fewest significant figures) is generally used.

Meaningful numbers in computation

Numbers consisting of digits that are significant relative to a measurement or other given number, indicating the degree of significance.

Least number of significant figures in a computation

The smallest number of digits in the numbers appearing in the answer, excluding exponents and roots.

Significant figures in a single computation

The final answer has the same number of significant figures as the least number of significant figures occurring in the values of the numbers appearing in the computation.

Significant figures in a series of computations

Carry at least the largest number of significant figures until the final answer is computed, then round off to the least number of significant figures appearing in the computation.

Decimal places vs. significant figures

They are not the same; a number can have the same decimal places but different significant figures (e.g., 0.324 (3SF), 2.004 (4SF), 23.450 (5SF) all have 3 decimal places).

Importance of units in engineering technology

Units are language expressions of the fundamental dimensions associated with the 'physics' of a quantity.

Six fundamental dimensions of physical quantities

Force, Mass, Length, Time, Temperature, Angle.

Two systems for physical quantities in the U.S.

S.I. (Système international d'unités, metric system) and U.S. Customary System.

SI units for fundamental dimensions

Force (Newton or kg×m/s²), Mass (kilogram), Length (meter), Time (second), Temperature (K or °C), Angle (rad or °).

U.S. Customary units for fundamental dimensions

Force (pound-force), Mass (slug or lbf×sec²/ft), Length (foot), Time (second), Temperature (°R or °F), Angle (rad or °).

Misunderstanding between force and mass (in unit conversion)

Force in SI (Newton) is derived (kg-m/s²), while Mass in US Customary (Slug) is derived (lbf-s²/ft).

Unit Abbreviations

Shorthand symbols used to represent full unit names (e.g., atm for atmosphere, km for kilometer, lbf for pound-force).

SI prefixes

Factors of ten used to denote magnitudes of units (e.g., tera (10¹²), giga (10⁹), mega (10⁶), kilo (10³), centi (10⁻²), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹), pico (10⁻¹²)).

Unit Conversion

Changing a unit from one expression to another without altering the fundamental dimensions.

Unit Conversion Factor

A ratio numerically equal to 1, used to convert units (e.g., 12 inches / 1 foot).

Factor-Label Method

A process of converting units using Unit Conversion Factors by multiplying the given value by ratios that equal one, ensuring units cancel out appropriately.

Non-proportional unit conversion

Conversions where the relationship is not a simple multiplicative factor, such as temperature conversions.

Celsius to Fahrenheit conversion formula

T(°F) = 1.8 T(°C) + 32

Celsius to Kelvin conversion formula

T(K) = T(°C) + 273.16

Fahrenheit to Rankine conversion formula

T(°R) = T(°F) + 459.69

Kelvin to Rankine conversion formula (absolute temperature)

T(°R) = 1.8[T(K)]