Lecture Notes Vocabulary: Scientific Notation, Accuracy/Precision, Significance, and Vectors

40 vocabulary flashcards covering scientific notation basics, accuracy vs. precision, significant figures, and vector concepts.

Scientific notation

A way to write very large or very small numbers as a coefficient between 1 and 10 multiplied by 10 raised to an exponent.

Coefficient

The number between 1 and 10 in scientific notation (the multiplier).

Exponent

The power of 10 in scientific notation indicating the scale of the number.

Base (in scientific notation)

The base used in scientific notation, typically 10.

Positive exponent

An exponent with a positive sign, indicating a large magnitude.

Negative exponent

An exponent with a negative sign, indicating a small magnitude.

Left = positive, Right = negative (exponent convention)

A sign convention indicating which side of the exponent is positive or negative.

Theoretical value

The accepted true value used as a standard for comparison.

Experimental value

The value measured or obtained from an experiment.

Percent error

(|Theoretical − Experimental| / Theoretical) × 100%, a measure of accuracy.

Accuracy

How close a measurement is to the actual or true value.

Precision

How finely measurements are made or how close repeated measurements are to each other.

Significant figures

Digits that carry meaningful information about precision in a measurement.

Non-zero digits are significant

All digits 1–9 are significant in a measurement.

Zeros between non-zero digits are significant

Zeros that occur between nonzero digits are counted as significant.

Leading zeros are not significant

Zeros to the left of the first nonzero digit do not count as significant.

Trailing zeros after a decimal point are significant

Zeros at the end of a number after the decimal point are significant.

Filler zeros to the left of decimal (not significant)

Leading zeros before the first nonzero digit are not significant.

Vector quantity

A physical quantity that has both magnitude and direction.

Scalar quantity

A physical quantity that has magnitude only.

Velocity

A vector quantity describing speed with a direction.

Weight

A vector quantity representing force due to gravity on a mass.

Friction

A vector quantity representing resistance to motion between surfaces.

Distance

A scalar quantity representing total ground covered during motion.

Displacement

A vector quantity representing the overall change in position from start to end.

Magnitude

The size or length of a vector or quantity.

Direction

The orientation a vector points toward.

Directed line segment

A vector drawn as an arrow with a tail (initial point) and head (final point).

Vector addition

The process of combining two or more vectors to produce a resultant vector.

Resultant

The overall vector obtained from adding two or more vectors.

Cancellation (vectors cancel each other out)

Two equal vectors in opposite directions sum to zero.

Perpendicular vectors

Vectors that are at right angles to each other.

Pythagorean theorem

In a right triangle, a^2 + b^2 = c^2; used to find vector magnitudes from perpendicular components.

Hypotenuse (in vector context)

The resultant magnitude in a right-triangle decomposition of a vector.

Components

The horizontal and vertical projections of a vector along perpendicular axes.

Vector resolution

The process of breaking a vector into its components along perpendicular directions.

SOH CAH TOA

Mnemonic to remember sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent.

Sine

Trigonometric function relating opposite side to hypotenuse in a right triangle.

Cosine

Trigonometric function relating adjacent side to hypotenuse in a right triangle.

Tangent

Trigonometric function relating opposite side to adjacent side in a right triangle.

Arctangent

Inverse tangent function used to calculate an angle from a ratio of opposite to adjacent.

Direction angle

The angle a vector makes with a reference axis, determined from its components.