Multiples, Submultiples, Conversion Factors, and Scientific Notation

Vocabulary flashcards covering metric prefixes, orthographic conventions, conversion factor techniques, and scientific notation operations based on the lecture notes.

Multiples

Units and prefixes used to express quantities that are larger than the reference unit.

Submultiples

Units and prefixes used to express quantities that are smaller than the reference unit.

Tera ($T$)

A metric multiple prefix representing an equivalence of $10^{12}$ or $1\,000\,000\,000\,000$ times the reference unit.

Giga ($G$)

A metric multiple prefix representing an equivalence of $10^9$ or $1\,000\,000\,000$ times the reference unit.

Mega ($M$)

A metric multiple prefix representing an equivalence of $10^6$ or $1\,000\,000$ times the reference unit.

Kilo ($k$)

A metric multiple prefix representing an equivalence of $10^3$ or $1000$ times the reference unit.

Hecto ($h$)

A metric multiple prefix representing an equivalence of $10^2$ or $100$ times the reference unit.

Deca ($da$)

A metric multiple prefix representing an equivalence of $10^1$ or $10$ times the reference unit.

Deci ($d$)

A metric submultiple prefix representing an equivalence of $10^{-1}$ or $0.1$ of the reference unit.

Centi ($c$)

A metric submultiple prefix representing an equivalence of $10^{-2}$ or $0.01$ of the reference unit.

Milli ($m$)

A metric submultiple prefix representing an equivalence of $10^{-3}$ or $0.001$ of the reference unit.

Micro ($\mu$)

A metric submultiple prefix representing an equivalence of $10^{-6}$ or $0.000\,001$ of the reference unit.

Nano ($n$)

A metric submultiple prefix representing an equivalence of $10^{-9}$ or $0.000\,000\,001$ of the reference unit.

Pico ($p$)

A metric submultiple prefix representing an equivalence of $10^{-12}$ or $0.000\,000\,000\,001$ of the reference unit.

Prefix Orthographic Rules

Guidelines establishing that full prefix names are written in lowercase, submultiple symbols are written in lowercase, and multiple symbols are written in uppercase with the exceptions of $da$ (deca), $h$ (hecto), and $k$ (kilo).

Conversion Factor

A fraction in which the numerator and the denominator represent equal measurements expressed in different units, used to change between units by canceling unwanted units.

Scientific Notation

A standard method for expressing very large or very small numbers using a figure between $1$ and $9$ followed by a decimal separator and decimal figures, multiplied by a power of $10$.

Addition and Subtraction in Scientific Notation

Mathematical operations performed on numbers with identical powers of $10$ by adding or subtracting the coefficients while retaining the shared power of $10$ (for example, $(2.55 \times 10^{-5}) + (1.42 \times 10^{-5}) = (2.55 + 1.42) \times 10^{-5} = 3.97 \times 10^{-5}$).

Multiples

Unit prefixes utilized to represent measurements and quantities that are greater than the reference unit.

Submultiples

Unit prefixes utilized to represent measurements and quantities that are smaller than the reference unit.

Tera ($\text{T}$)

A multiple prefix with an equivalence of $10^{12}$ ($1\,000\,000\,000\,000$) relative to the reference unit.

Giga ($\text{G}$)

A multiple prefix with an equivalence of $10^9$ ($1\,000\,000\,000$) relative to the reference unit.

Mega ($\text{M}$)

A multiple prefix with an equivalence of $10^6$ ($1\,000\,000$) relative to the reference unit.

Kilo ($\text{k}$)

A multiple prefix with an equivalence of $10^3$ ($1\,000$) relative to the reference unit.

Hecto ($\text{h}$)

A multiple prefix with an equivalence of $10^2$ ($100$) relative to the reference unit.

Deca ($\text{da}$)

A multiple prefix with an equivalence of $10^1$ ($10$) relative to the reference unit.

Deci ($\text{d}$)

A submultiple prefix with an equivalence of $10^{-1}$ ($0.1$) relative to the reference unit.

Centi ($\text{c}$)

A submultiple prefix with an equivalence of $10^{-2}$ ($0.01$) relative to the reference unit.

Milli ($\text{m}$)

A submultiple prefix with an equivalence of $10^{-3}$ ($0.001$) relative to the reference unit.

Micro ($\mu$)

A submultiple prefix with an equivalence of $10^{-6}$ ($0.000001$) relative to the reference unit.

Nano ($\text{n}$)

A submultiple prefix with an equivalence of $10^{-9}$ ($0.000000001$) relative to the reference unit.

Pico ($\text{p}$)

A submultiple prefix with an equivalence of $10^{-12}$ ($0.000000000001$) relative to the reference unit.

Prefix Orthographic Rules

The spelling standard dictating that prefix names are written in lowercase, submultiple symbols are written in lowercase, and multiple symbols are written in uppercase, except for deca ($\text{da}$), hecto ($\text{h}$), and kilo ($\text{k}$).

Liter to Cubic Decimeter Equivalence

The metric volume equivalence stating that $1\,\text{dm}^3 = 1\,\text{L}$.

Conversion Factor

A fraction in which the numerator and denominator represent equal quantities expressed in different units, used to convert measurements between units or multiples and submultiples.

Inverted Fraction

A conversion factor arranged with the original unit in the numerator and the new unit in the denominator, utilized when changing units located in the denominator of a compound unit (such as hours in $\text{km/h}$).

Unit Cancellation

The elimination of identical units appearing in both the numerator and the denominator of a conversion expression, verifying the conversion factor is correct.

Scientific Notation

A standardized method for expressing very large or very small numbers, consisting of a number between $1$ and $9$ followed by decimal places, multiplied by an integer power of $10$.

Addition with Equal Powers of Ten

A scientific notation rule in which terms sharing identical powers of $10$ have their decimal coefficients added together directly while retaining the common power of $10$, as in $2.55 \times 10^{-5} + 1.42 \times 10^{-5} = (2.55 + 1.42) \times 10^{-5} = 3.97 \times 10^{-5}$.

Subtraction with Equal Powers of Ten

A scientific notation rule in which terms sharing identical powers of $10$ have their decimal coefficients subtracted while retaining the common power of $10$, as in $2.55 \times 10^{-5} - 1.42 \times 10^{-5} = (2.55 - 1.42) \times 10^{-5} = 1.13 \times 10^{-5}$.