Quantities Representation

Quantities representation is the mathematical use of numbers, symbols, units, diagrams, tables, and graphs to describe how much of something exists or how quantities relate. It works by assigning values to measurable attributes, choosing an appropriate scale or notation, and transforming the same information among forms such as fractions, decimals, percentages, equations, coordinate plots, and proportional relationships. In mathematics, these representations help students interpret magnitude, compare values, identify patterns, and communicate reasoning while supporting applications in measurement, data analysis, modeling, and quantitative decision-making. Selecting a representation that matches the problem can reveal relationships that are less visible in another form.

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JoVE Core - Physics

Base Quantities and Derived Quantities

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2023

In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities of the system, and their units are the base units of the system. The algebraic combinations of the base values can then be used to express all other physical quantities. Each of these physical quantities is then referred to as a derived quantity, with each unit being referred to as a derived unit. The International Organization for...

Economic Order Quantity

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2025

Commercial distributors often face a trade-off between ordering frequency and inventory holding. Ordering too often inflates administrative costs, while infrequent bulk orders tie up capital in storage and insurance. The Economic Order Quantity (EOQ) model provides a quantitative approach to striking this balance, allowing firms to identify the order size that minimizes the combined costs of ordering and holding inventory.The EOQ formula can be simplified into plain language for easier...

The Quantity of Money

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2025

The quantity of money, or money supply, is the total amount of money available in an economy. In modern economies, defining and measuring the money supply is a challenge due to the wide variety of assets used as money.Unlike a simple system with only one form of money, today's economies feature multiple forms of money that people can access through various channels.For example, people often use cash or a debit card for everyday expenses, such as buying groceries. The debit card directly...

State Space Representation

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2024

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system. Consider an RLC circuit, a...

Control Volume and System Representations

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2025

Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach). The control volume approach considers a stationary region in space through which fluid flows. This region is bounded by a control surface. For instance, in the case of water flowing...

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