Coefficient Meaning: Definition, Examples, and Translations
๐ข
coefficient
[kษสษชหfษชสษnt ]
Definitions
mathematics
A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Synonyms
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.
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| 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.
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| 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.
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| 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.
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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.
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.
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| 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.
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| 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.
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Examples of usage
- The coefficients in the balanced equation 2Hโ + Oโ โ 2HโO 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.
Translations
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Interesting Facts
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 equationโs 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.
Origin of 'coefficient'
Main points about word origin
- 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.
The word 'coefficient' originated from the Latin word 'coefficientem', which means 'a co-efficient or concurrence'. It entered the English language in the 17th century. The concept of coefficients has been crucial in various fields such as mathematics, physics, chemistry, and economics, where they play a fundamental role in equations, formulas, and calculations.