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3: Measurements

Last updated

Mar 21, 2025
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- 2.18: Recognizing Chemical Reactions
- 3.1: SI Base Units

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Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

3.1: SI Base Units
This page discusses the historical definition and evolution of the yard, initially tied to royal measurements but now standardized. It highlights the challenges of the English measurement system for scientific purposes, leading to the adoption of the metric system in 1795 and the International System of Units (SI) established in 1960. Although the U.S. has legally adopted the metric system, it predominantly uses the imperial system.
3.2: Metric Prefixes
This page discusses the significant influence of Latin and Greek on modern scientific and legal terminology, particularly through metric prefixes like kilo and mega. It emphasizes the clarity and ease of communication afforded by the metric system's straightforward conversions based on powers of ten and underscores the importance of using appropriate units and adhering to conventions for metric abbreviations.
3.3: Scientific Notation
This page explains scientific notation for expressing large and small numbers using a coefficient and a power of ten, exemplified by the distance from Earth to the Sun (150 million km as $1.5 \times 10^{11}$ meters). It covers SI prefixes from giga to pico, showing their relationship to measurements in multiples and fractions of ten. Scientific notation simplifies handling extreme values by offering a structured representation.
3.4: Length and Volume
This page discusses traditional and modern methods of measuring sea depths, explaining that sailors used fathoms and a knotted rope, while current approaches utilize electronic instruments. It also defines length and volume, highlighting the meter as the SI unit for length and the cubic meter for volume, along with practical measurements like liters and milliliters used in labs.
3.5: Mass and Weight
This page explores weightlessness in outer space and its effects on astronauts' bone health. It clarifies the difference between mass, a constant measure of matter, and weight, which is influenced by gravity. The text also mentions that weight is less on the moon than on Earth, while mass stays the same regardless of location. Additionally, it gives a brief explanation of how to measure mass and weight.
3.6: Kinetic Energy
This page explains energy as the capacity to perform work or produce heat, detailing kinetic energy as energy due to motion with the formula KE = 1/2 mv², where m is mass and v is velocity. It also describes potential energy as stored energy, and notes the joule (J) as the SI unit of energy, with calories as a common alternative unit (1 cal = 4.184 J).
3.7: Temperature and Temperature Scales
This page explains temperature as a measure of average kinetic energy, describing the Fahrenheit, Celsius, and Kelvin scales, including their freezing and boiling points. It notes that Celsius and Kelvin are related by 273 and emphasizes the simplicity of conversions between these scales. Additionally, it mentions the historical development and relevance of these temperature scales in the field of chemistry.
3.8: Dimensional Analysis
This page explains conversion factors as ratios of equivalent measurements, highlighting the consistency of quantity despite varying numerical values in different units like cups and pints. It introduces dimensional analysis for problem-solving using measurement units, exemplified by calculating the number of seconds in a day, illustrating how units cancel out to yield a final answer in the desired unit.
3.9: Metric Unit Conversions
This page explains converting track laps to distance using dimensional analysis and metric conversions, emphasizing metric prefixes. It includes examples for calculating milliliters for experiments and converting centimeters to micrometers. The importance of unit sizes and proper cancellation during conversions is highlighted, alongside a review section for additional practice on unit conversions.
3.10: Derived Units
This page covers the evolution of farming, focusing on the increasing trend of farmers selling land for development amid rising costs and declining profits for small farms. It also explains derived units in the metric system, detailing the importance of dimensional analysis for unit conversions, with practical examples and a step-by-step process from cubic millimeters to milliliters. The conclusion emphasizes the significance of understanding derived units in measurements.
3.11: Density
This page explains density as the ratio of mass to volume and its role in buoyancy, noting that it remains constant across sample sizes but can vary with temperature. It presents examples of densities of common substances, highlighting that gases are less dense than solids and liquids. The text includes calculations and problem-solving methods related to density, underscoring its practical applications in measuring mass and volume.
3.12: Accuracy and Precision
This page discusses the importance of accuracy and precision in professional basketball shooting. Accuracy measures how close a shot lands to the basket, while precision refers to the consistency of shots. Using dartboard examples, the text emphasizes that high precision does not ensure accuracy and that both are vital for success in basketball and scientific measures. Athletes and scientists work to improve both aspects in their respective fields.
3.13: Percent Error
This page discusses the role of resistors in electrical circuits for regulating voltage and current, emphasizing the significance of understanding their values and error ranges for equipment functionality. It defines "accepted value" and "experimental value," and demonstrates how to calculate error and percent error using aluminum density as an example. As measurement accuracy diminishes, the percent error rises, indicating reduced precision.
3.14: Measurement Uncertainty
This page discusses how police identify criminals through witness descriptions, focusing on the inherent uncertainty in measurements like height due to the quality of tools and the skill of the measurer. It emphasizes that precise tools, such as rulers with detailed markings, can improve measurement accuracy and reduce uncertainty, highlighting their significance in effective assessments.
3.15: Rounding
This page discusses the practice of rounding numbers, especially regarding significant figures. It explains how people simplify measurements for easier communication, as seen in examples involving fishermen. The text highlights the relationship between rounding and precision, noting that increased rounding can diminish accuracy. It underscores the importance of grasping rounding rules for scientific precision.
3.16: Significant Figures
This page explains significant figures in measurements, focusing on their role in indicating certainty. It outlines rules for identifying significant figures, including the treatment of various zeros. The text explains that insignificant zeros are placeholders and cannot be excluded. It also highlights the utility of scientific notation in representing significant figures accurately. The page concludes with a summary and review questions to reinforce understanding.
3.17: Significant Figures in Addition and Subtraction
This page discusses the importance of accuracy in numerical computations using calculators, emphasizing that results should be rounded to reflect the precision of the least precise measurement in addition or subtraction. For instance, when adding 16.7 g and 5.24 g, the answer should be reported as 21.9 g. This rounding principle also applies to whole numbers, with results adjusted to the last significant digit of the input values.
3.18: Significant Figures in Multiplication and Division
This page explains that calculators provide exact numerical results without considering significant figures, requiring users to report results based on the least precise measurement. For multiplication and division, results should reflect the significant figures of the least precise measurement. It includes examples and exercises to highlight the importance of rounding and correct unit usage in calculations and presentations.

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