Coefficient: meaning, definitions and examples

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coefficient

[kəʊɪˈfɪʃənt ]

Definitions

^{Context #1 | Noun}

mathematics

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Synonyms

constant, factor, multiplier.

Which Synonym Should You Choose?

Word	Description / Examples
coefficient	Used in mathematics and physics to indicate a numerical value that multiplies a variable. Most commonly used in algebraic expressions, equations, and in certain scientific contexts. In the equation 3x + 4 = 10, the number 3 is the coefficient of x. The friction coefficient between the two surfaces is 0.5.
factor	Used to describe a number or quantity that, when multiplied with another, produces a given number. Often used in both mathematics and general conversation to signify an element that contributes to a result. In the equation 2 * 3 = 6, both 2 and 3 are factors of 6. Exercise is a crucial factor in maintaining good health.
multiplier	Refers to a number by which another number is multiplied. Often used in mathematics and economics to describe the effect of one quantity multiplying another. In the multiplication problem 4 * 5 = 20, the number 4 is the multiplier. The economic multiplier effect can amplify the impact of government spending.
constant	Refers to a fixed value that does not change. Commonly used in mathematics to refer to a value in an equation or expression that remains the same. The value of π (pi) is a constant, approximately equal to 3.14159. In the formula y = mx + c, 'c' is the constant term.

Examples of usage

The coefficient of x in the expression 3x + 5 is 3.
Higher coefficients indicate a larger impact on the overall result.
The coefficient of friction is a key factor in determining the force required to move an object.

^{Context #2 | Noun}

chemistry

In chemistry, a coefficient is a number placed in front of a chemical formula in a balanced equation, representing the stoichiometry of the reaction.

Synonyms

mole ratio, stoichiometric coefficient.

Which Synonym Should You Choose?

Word	Description / Examples
coefficient	Used in mathematics and science to refer to a numerical or constant quantity placed before and multiplying the variable in an algebraic expression, equation, or term. In the equation 3x + 2, the number 3 is the coefficient of x. We calculated the correlation coefficient to understand the relationship between variables.
stoichiometric coefficient	Used in chemistry to refer to the numbers in front of molecules in a balanced chemical equation, representing the ratio in which reactants and products participate in the reaction. In H2 + O2 -> H2O, the stoichiometric coefficients are 1 for H2, 1 for O2, and 2 for H2O. To balance the reaction, you need to adjust the stoichiometric coefficients.
mole ratio	Specifically used in chemistry to describe the ratio of moles of one substance to the moles of another substance in a chemical reaction. Often used in stoichiometry to balance equations and make predictions about reactions. In the balanced equation, the mole ratio of hydrogen to oxygen is 2:1. We need to take into account the mole ratio to determine how much product will be formed.

Word

Description / Examples

coefficient

Used in mathematics and science to refer to a numerical or constant quantity placed before and multiplying the variable in an algebraic expression, equation, or term.

In the equation 3x + 2, the number 3 is the coefficient of x.
We calculated the correlation coefficient to understand the relationship between variables.

stoichiometric coefficient

Used in chemistry to refer to the numbers in front of molecules in a balanced chemical equation, representing the ratio in which reactants and products participate in the reaction.

In H2 + O2 -> H2O, the stoichiometric coefficients are 1 for H2, 1 for O2, and 2 for H2O.
To balance the reaction, you need to adjust the stoichiometric coefficients.

mole ratio

Specifically used in chemistry to describe the ratio of moles of one substance to the moles of another substance in a chemical reaction. Often used in stoichiometry to balance equations and make predictions about reactions.

In the balanced equation, the mole ratio of hydrogen to oxygen is 2:1.
We need to take into account the mole ratio to determine how much product will be formed.

Examples of usage

The coefficients in the balanced equation 2H₂ + O₂ → 2H₂O indicate the mole ratios of the reactants and products.
Balancing chemical equations involves adjusting the coefficients to ensure mass conservation.
A stoichiometric coefficient of 1 implies a one-to-one ratio in the reaction.

Interesting Facts

Etymology

The word comes from the Latin 'coefficientem', meaning 'working together'.
The prefix 'co-' means 'together', while 'efficient' relates to being effective or capable.
It first appeared in use in the early 19th century, linking it to the growth of algebra.

Mathematics

In an equation like 3x + 4 = 10, the number 3 is the coefficient of x.
Coefficients can be negative, positive, or even zero, affecting the equation’s solution differently.
In polynomials, coefficients can represent real numbers, but they can also be complex numbers in more advanced mathematics.

Science

In physics, coefficients often represent ratios or constants, like friction or thermal conductivity.
The concept is crucial in statistics, where coefficients can describe relationships between variables in regression analysis.
Coefficients in chemistry can indicate the ratio of molecules in a reaction, which is essential for balancing equations.

Technology

In computer science, coefficients help optimize algorithms in data analysis and machine learning.
Image processing uses coefficients in techniques like Fourier transforms to analyze signals and images.
In coding, functions often rely on coefficients to adjust parameters dynamically based on user input.

Cultural Impact

Educational systems worldwide emphasize the importance of learning about coefficients for higher-level mathematics.
Many careers in engineering and technology require a solid understanding of coefficients in practical applications.
Pop culture references math terms like coefficients in movies or books to convey intelligence or technical prowess.

Translations

Translations of the word "coefficient" in other languages:

🇵🇹 coeficiente

🇮🇳 गुणांक

🇩🇪 Koeffizient

🇮🇩 koefisien

🇺🇦 коефіцієнт

🇵🇱 współczynnik

🇯🇵 係数

🇫🇷 coefficient

🇪🇸 coeficiente

🇹🇷 katsayı

🇰🇷 계수

🇸🇦 معامل

🇨🇿 koeficient

🇸🇰 koeficient

🇨🇳 系数

🇸🇮 koeficient

🇮🇸 stuðull

🇰🇿 коэффициент

🇬🇪 კოეფიციენტი

🇦🇿 əmsal

🇲🇽 coeficiente

Word Frequency Rank

Ranking #3,283, this word is part of upper-intermediate vocabulary. While not among the most basic terms, it appears often enough to be valuable for advanced communication.

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