# Numerical coefficient

A numerical factor that multiplies another factor in a term is called a numerical coefficient.

## Introduction

A term is usually formed by the product of a number and one or more other factors. It is actually determined in any type of term on two characteristics.

1. It should be in numerical form (number).
2. It should multiply other type of factor/ factors in a term.

### Examples

The concept of numerical coefficient is appeared in all topics of the mathematics. The numerical portion in a term is identified to determine the numerical coefficient in the respective term. The following examples help you to understand how to determine numerical coefficient in any type of term in mathematics.

$(1) \,\,\,$ $-7x^2y$

It is an algebraic term. It displays two numbers $-7$ and $2$ but $2$ is an exponent and not a multiplying factor. Write the term in product form as $-7 \times x^2y$. Therefore, $-7$ is a number and multiplies $x^2y$. So, $-7$ is called as numerical coefficient of $x^2y$.

$(2) \,\,\,$ $0.75\log_{6}{y}$

It is a log term. It shows two numbers $0.75$ and $6$ but $6$ is a base of the logarithmic term and it is not multiplying anything. Write, the logarithmic term in product form. It means $0.75\log_{6}{y} \,=\, 0.75 \times \log_{6}{y}$.

In this term, $0.75$ is a number in decimal form and multiplies the factor $\log_{6}{y}$. So, it is obvious that $0.75$ is a numerical coefficient of $\log_{6}{y}$.

$(3) \,\,\,$ $2\sin{x}\cos{x}$

It is a trigonometric term. Separate the numerical portion from the other trigonometric factors by writing it in product form.

$2\sin{x}\cos{x}$ $\,=\,$ $2 \times \sin{x}\cos{x}$

Therefore, $2$ is known as numerical coefficient of $\sin{x}\cos{x}$.

$(4) \,\,\,$ $\dfrac{9}{14}\dfrac{dy}{dx}$

It is a differential term in which a fraction $\dfrac{9}{14}$ is multiplying remaining factor in differential form. Therefore, $\dfrac{9}{14}$ is called as numerical coefficient of $\dfrac{dy}{dx}$.

Thus, the numerical coefficients are determined in all kinds of terms in mathematics.

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Jun 26, 2023

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