Math Notes - Percent Change, Scientific Notation, and Unit Conversions

Vocabulary flashcards defining key math formulas, scientific notation rules, and unit conversion methods from the lecture notes.

Percent Change

A calculation to find the relative change between values using the formula $\frac{\text{New} - \text{Old}}{\text{Old}} \times 100$.

Scientific Notation

A method to write numbers by moving the decimal point so that there is only one non-zero digit to the left of the decimal, expressed as $a \times 10^n$, where $1 \le a < 10$ and $n$ is the number of places the decimal point was moved.

Percent Increase

A measure of percentage growth defined by the formula $\frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%$.

Percent Decrease

A measure of percentage reduction defined by the formula $\frac{\text{Original Value} - \text{New}}{\text{Original}} \times 100$.

Scientific Notation (Positive Exponent Example)

Moving the decimal $3$ places to the left converts $4,500$ to $4.5 \times 10^3$ ($n = 3$).

Scientific Notation (Negative Exponent Example)

Moving the decimal $5$ places to the right converts $0.000045$ to $4.5 \times 10^{-5}$ ($n = -5$).

Unit Conversion (Kilometers to Meters)

Converting $12\,\text{km}$ to meters using conversion factors: $12\,\text{km} \times \frac{1000\,\text{m}}{1\,\text{km}} = 12,000\,\text{m}$.

Unit Conversion (Years to Seconds)

Converting $1.5\,\text{yrs}$ to seconds using conversion factors: $1.5\,\text{yrs} \times \frac{365.25}{1\,\text{yr}} \times \frac{24}{1} \times \frac{3600}{1} = 47,304,000\,\text{sec}$.