Scientific Notation, SI Units, and Dimensional Analysis Flashcards

Vocabulary flashcards covering core topics from Chapters 1 through 7 of the lecture transcript, including scientific notation, significant digit rules, SI base and derived units, prefixes, temperature conversions, and dimensional analysis.

Scientific Notation

A standard numerical format written as $a \times 10^y$, where $a$ (the mantissa or significand) is a single number from 1 to 9 to the left of the decimal point, and $y$ is an exponent representing scale.

Mantissa (Significand)

The numerical factor $a$ located in front of the multiplication sign in scientific notation ($a \times 10^y$), which must contain exactly one non-zero digit (1 through 9) to the left of the decimal point.

Significant Digits

Formally defined as all digits in a measurement that are known with certainty plus one final digit that contains a nominal amount of error.

Rounding Rule for Multiplication and Division

A rounding rule specifying that the final calculated answer must be rounded to match the minimum number of significant digits present in any of the starting variables.

Rounding Rule for Addition and Subtraction

A rounding rule specifying that the final calculated answer must be rounded to match the minimum number of decimal places present in any of the starting values.

Five-Rounding Rule (Round to Even)

A rounding convention applied when the digit to the right of the last significant digit is exactly 5 (or 5 followed only by zeros), requiring the last significant digit to be rounded to the nearest even number.

International System of Units (SI)

The standardized scientific system of measurement used worldwide, consisting of seven fundamental base units along with derived units.

Kilogram

The SI base unit for mass (symbol: $\text{kg}$); it is unique as the only SI base unit defined with a prefix value.

Candela

The SI base unit used to measure luminous intensity, represented by the symbol $\text{cd}$.

Mole

The SI base unit used to represent the amount of a substance, represented by the symbol $\text{mol}$.

Derived Units

Units produced by combining two or more SI base units, such as meters per second ($\text{m\,s}^{-1}$) for speed or cubic meters ($\text{m}^3$) for volume.

Deci-

An SI prefix representing a factor of $10^{-1}$, denoted by the lowercase symbol $\text{d}$.

Kilo-

An SI prefix representing a factor of $10^3$, denoted by the lowercase symbol $\text{k}$.

Pico-

An SI prefix representing a factor of $10^{-12}$, denoted by the lowercase symbol $\text{p}$.

Giga-

An SI prefix representing a factor of $10^9$, denoted by the uppercase symbol $\text{G}$.

Micro-

An SI prefix representing a factor of $10^{-6}$, denoted by the Greek character $\mu$.

Peta-

An SI prefix representing a factor of $10^{15}$, denoted by the uppercase symbol $\text{P}$.

Nano-

An SI prefix representing a factor of $10^{-9}$, denoted by the lowercase symbol $\text{n}$.

Kelvin Conversion Formula

The equation $T_{\text{K}} = 273.15 + T_{^{\circ}\text{C}}$ used to convert temperature from degrees Celsius to Kelvin ($\text{K}$), the SI base unit for temperature.

Fahrenheit Conversion Formula

The equation $T_{^{\circ}\text{F}} = (T_{^{\circ}\text{C}} \times 1.8) + 32$ used to convert temperature from degrees Celsius to degrees Fahrenheit.

Exact Values

Numbers in mathematical equations (such as $1.8$ and $32$ in temperature conversions) that possess an infinite number of significant digits and do not limit the precision of a calculated answer.

Dimensional Analysis

A problem-solving method that organizes unit relationships first to build a correct structural calculation before inserting numerical values.

Trapped Zeros

Zeros located between non-zero digits (e.g., the zero in $8.02$) that are always counted as significant digits.

Trailing Zeros with Decimal Points

Zeros appearing at the end of a number after non-zero digits that are significant if an explicit decimal point is present.