Lecture 2: Basic Measurements

This flashcard set covers the basic measurements lecture including SI units, significant figure rules, unit conversion failures, and dimensional analysis.

Mars Climate Orbiter

A $125$ million spacecraft lost in 1999 due to a failure to convert English units (thrust data from Lockheed Martin) to metric units used by NASA scientists.

International System of Units (SI)

The globally agreed-upon standard for scientific measurements, built upon seven fundamental base units.

Derived units

Physical measurements, such as velocity, force, or volume, calculated by combining the seven fundamental base dimensions.

SI prefixes

Scales added directly to unit names (e.g., kilometer, milligram) to scale base units by powers of 10 for expressing very large or very small numbers.

Significant figures

The meaningful digits in a measured or calculated value that reflect the precision of the instruments used.

Leading zeros

Zeros that precede all nonzero digits; they function only to indicate the position of the decimal point and do not count as significant figures (e.g., $0.0025$ has two significant figures).

Captive zeros

Zeros located between nonzero digits which always count as significant figures (e.g., $1.008$ has four significant figures).

Trailing zeros

Zeros at the right end of a number that are significant only if the number contains a decimal point (e.g., $100$ has one significant figure, while $100.$ has three).

Exact numbers

Numbers determined by counting (e.g., $3$ apples) or by definition (e.g., $1\text{ in} = 2.54\text{ cm}$); they are assumed to have an infinite number of significant figures.

Significant Figures: Addition and Subtraction Rule

The answer is rounded to the same number of decimal places as the value with its rightmost significant figure in the greatest decimal place.

Significant Figures: Multiplication and Division Rule

The answer is rounded to the same number of significant figures as the value in the problem with the least number of significant figures.

Rounding (Less than 5)

If the digit to be removed is less than 5, the preceding digit remains the same.

Rounding (Equal to or greater than 5)

If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1.

Dimensional analysis

Also known as the unit factor method, this is a procedure used to convert a result from one system of units to another.

Temperature scales

The three systems used for measurement are Celsius, Kelvin, and Fahrenheit; Celsius and Kelvin are used in physical sciences, while Fahrenheit is used in engineering.

Gas Constant ($R$) formula

A calculation defined as $R = \frac{PV}{T}$, where $P$ is pressure, $V$ is volume, and $T$ is temperature.