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# 1.5: Units and Measurement Redux

The thumbnail image is of the Whirlpool Galaxy, which we examine in the first section of this chapter. Galaxies are as immense as atoms are small, yet the same laws of physics describe both, along with all the rest of nature—an indication of the underlying unity in the universe. The laws of physics are surprisingly few, implying an underlying simplicity to nature’s apparent complexity. In this text, you learn about the laws of physics. Galaxies and atoms may seem far removed from your daily life, but as you begin to explore this broad-ranging subject, you may soon come to realize that physics plays a much larger role in your life than you first thought, no matter your life goals or career choice.

• Dimensional Analysis
The dimension of a physical quantity is just an expression of the base quantities from which it is derived. All equations expressing physical laws or principles must be dimensionally consistent. This fact can be used as an aid in remembering physical laws, as a way to check whether claimed relationships between physical quantities are possible, and even to derive new physical laws.
• Estimates and Fermi Calculations
An estimate is a rough educated guess at the value of a physical quantity based on prior experience and sound physical reasoning. Some strategies that may help when making an estimate are as follows: 1) Get big lengths from smaller lengths. 2) Get areas and volumes from lengths. 3) Get masses from volumes and densities. 4) If all else fails, bound it. One “sig. fig.” is fine. 5) Ask yourself: Does this make any sense?
• Prelude to Units and Measurement
The laws of physics are surprisingly few, implying an underlying simplicity to nature’s apparent complexity. In this text, you learn about the laws of physics. Galaxies and atoms may seem far removed from your daily life, but as you begin to explore this broad-ranging subject, you may soon come to realize that physics plays a much larger role in your life than you first thought, no matter your life goals or career choice.
• Significant Figures
Accuracy of a measured value refers to how close a measurement is to an accepted reference value. Precision of measured values refers to how close the agreement is between repeated measurements. Significant figures express the precision of a measuring tool. When performing mathematical operations with measured values, there are rules to standardize the precision of the final answer.
• Solving Problems in Physics
The three stages of the process for solving physics problems used in this textmap are as follows: 1)Strategy: Determine which physical principles are involved and develop a strategy for using them to solve the problem. 2) Solution: Do the math necessary to obtain a numerical solution with the correct units. 3) Significance: Check the solution to make sure it makes sense and assess its significance.
• The Scope and Scale of Physics
Physics is about trying to find the simple laws that describe all natural phenomena. It operates on a vast range of scales involving length, mass, and time. Scientists attempt to describe the world by formulating models, theories, and laws. They utilize orders of magnitudes of numbers to track and compare phenomena occurring on particular scales.