Ch 2. Measurement and Problem Solving

Flashcards covering measurement uncertainty, scientific notation, significant figures, SI units, and problem-solving techniques from Chapter 2.

Uncertainty

The degree of doubt in a measurement, indicated by the last reported digit which is estimated (e.g., a report of $0.6 \text{ }^{\circ}\text{C}$ means $0.6 \text{ +/- } 0.1 \text{ }^{\circ}\text{C}$).

Scientific Notation

A method of writing very large or very small numbers consisting of a decimal part (between 1 and 10) and an exponential part ($10^n$).

Decimal Part

In scientific notation, this is the number that is between 1 and 10.

Exponential Part

In scientific notation, this is $10$ raised to an exponent, $n$.

Positive Exponent (Scientific Notation)

Indicates that $1$ is multiplied by $10$, $n$ times; result of moving the decimal point to the left.

Negative Exponent (Scientific Notation)

Indicates that $1$ is divided by $10$, $n$ times; result of moving the decimal point to the right.

Significant Figures

The digits in a correctly reported measurement where the first four digits are certain and the last digit is estimated.

Interior Zeros

Zeros between two numbers that are always counted as significant.

Trailing Zeros (with decimal)

Zeros to the right of a nonzero number that fall after a decimal point; these are significant.

Leading Zeros

Zeros to the left of the first nonzero number; they are NOT significant and serve only to locate the decimal point.

Ambiguous Zeros

Trailing zeros at the end of a number but before an implied decimal point (e.g., $100,000$).

Exact Numbers

Numbers with an unlimited number of significant figures, such as discrete object counts, integral numbers in equations, or defined quantities like $1\,\text{in.} = 2.54\,\text{cm}$.

Multiplication and Division Rule

The rule stating research results carry the same number of significant figures as the factor with the fewest significant figures.

Addition and Subtraction Rule

The rule stating the result carries the same number of decimal places as the quantity carrying the fewest decimal places.

International System of Units (SI)

The unit system for science measurements based on the metric system (Système International d’Unités).

Meter (m)

The SI standard of length, defined as the distance that light travels in vacuum in $1/299,792,458\,\text{s}$.

Kilogram (kg)

The SI standard of mass, defined as the mass of a block of metal kept at the International Bureau of Weights and Measures at Sèvres, France.

Second (s)

The SI standard of time, defined as the duration of $9,192,631,770$ periods of radiation emitted from a cesium-133 atom transition.

Mass

A measure of the quantity of matter within an object.

Weight

A measure of the gravitational pull on the matter within an object.

Tera- (T)

SI prefix multiplier meaning trillion ($10^{12}$).

Giga- (G)

SI prefix multiplier meaning billion ($10^9$).

Mega- (M)

SI prefix multiplier meaning million ($10^6$).

Kilo- (k)

SI prefix multiplier meaning thousand ($10^3$).

Deci- (d)

SI prefix multiplier meaning tenth ($10^{-1}$).

Centi- (c)

SI prefix multiplier meaning hundredth ($10^{-2}$).

Milli- (m)

SI prefix multiplier meaning thousandth ($10^{-3}$).

Micro- (μ)

SI prefix multiplier meaning millionth ($10^{-6}$).

Nano- (n)

SI prefix multiplier meaning billionth ($10^{-9}$).

Pico- (p)

SI prefix multiplier meaning trillionth ($10^{-12}$).

Femto- (f)

SI prefix multiplier meaning quadrillionth ($10^{-15}$).

Derived Unit

A unit formed from other units, such as volume units formed by cubing units of length (e.g., $\text{m}^3$, $\text{cm}^3$).

Dimensional Analysis

The practice of using units as a guide to solving problems, where units are multiplied, divided, and canceled algebraically.

Solution Map

A visual outline that shows the strategic route and units required to convert from the starting information to the find quantity.

Density (d)

The ratio of a substance's mass to its volume, expressed as the equation $d = \frac{m}{V}$.