Name: measurement precision and significant figures
Uploaded: 2023-04-30T10:48:20.000Z
Duration: 1 min 44 s
Channel: JoVE

ודאות המדידה תלויה בשני גורמים: מספר הספרות במדידה ודיוק המכשיר בו נעשה שימוש.
בכמות מדודה, כל הספרות, כולל הספרה האחרונה שאינה ודאית, נקראות מספרים משמעותיים - וניתן לקבוע אותן באמצעות כללים ספציפיים.
כל הספרות שאינן אפס וכל האפסים השבויים - הנמצאים בין שתי ספרות שאינן אפס - הם משמעותיים. לדוגמה, 28 יש שתי דמויות משמעותיות, בעוד 26.25 יש ארבע, ו 208 יש שלוש.
אפסים מובילים לעולם אינם משמעותיים, מכיוון שהם פשוט ממקמים את הנקודה העשרונית. לדוגמה, 0.00208 יש שלוש דמויות משמעותיות. כמויות כאלה ניתן לבטא באמצעות סימונים מעריכיים. לפיכך, 0.00208 יכול להיכתב כ- 2.08 × 10−3.
אפסים נגררים משמעותיים רק במספרים עשרוניים מעוצבים. ל- 2200 יש שני אפסים נגררים ושתי ספרות משמעותיות, ואילו ל- 2200.0 ו- 2200.1 יש 5 מספרים משמעותיים.
עבור כמויות ללא נקודות עשרוניות, המשמעות של אפסים נגררים הופכת למעורפלת. לפיכך, 2200 יכול להיכתב כמו 2.2 × 103 עם שתי דמויות משמעותיות או 2.20 x 103 עם שלוש דמויות משמעותיות.

כללים לספירת ערכים

<div style="direction:rtl">בכל מדידה, הדיוק של כלי המדידה הוא גורם חיוני. סרגל רגיל, למשל, יכול למדוד אורך עד למילימטר הקרוב ביותר; קליפר, לעומת זאת, יכול למדוד אורך עד 0.01 מ"מ הקרוב ביותר. כתוצאה מכך, הקליפר הוא כלי מדידה מדויק יותר מכיוון שהוא יכול למדוד שינויים זעירים ביותר באורך. המדידות יהיו מדויקות יותר אם כלי המדידה יהיה מדויק יותר. יש להדגיש שכאשר אנו מייצגים ערכים נמדדים, הספרה האחרונה חושבה בדרך כלשהי על ידי מי שמבצע את המדידה. לדוגמה, אדם שמודד אורך של מקל עם סרגל שם לב שנראה שהוא בין 13.2 ס"מ ל-13.3 ס"מ, ולכן עליהם להעריך את ערך הספרה האחרונה. הכלל של נתונים משמעותיים הוא שהספרה האחרונה שנרשמת במדידה היא הספרה הראשונה עם אי ודאות מסוימת. התחל עם הערך הנמדד הראשון משמאל וספור את מספר הספרות עד הספרה האחרונה שנכתבה מימין כדי לקבוע את מספר הספרות המשמעותיות בערך. נתונים משמעותיים מייצגים את הדיוק של כלי המדידה המשמש למדידת ערך. הטקסט אומץ מ <a href="https://openstax.org/books/university-physics-volume-1/pages/1-6-significant-figures">Openstax, University Physics Volume 1, Section: 1.6 Significant Figures. </a></div>

בכל מדידה, הדיוק של כלי המדידה הוא גורם חיוני. סרגל רגיל, למשל, יכול למדוד אורך עד הקרוב ביותר ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Units, Dimensions, and Measurements

יחידות, ממדים ומדידות

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

Rules for Significant Figures

measurement precision and significant figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length.

When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must be recorded with a guessed last digit.

The last digit in a measurement is the first digit with some uncertainty. To find the number of significant figures, start with the first measured value on the left and count through the last digit written on the right. Significant figures show how precise the measuring tool was when the value was recorded.

Measurement Precision and Significant Figures

measurement-precision-and-significant-figures

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

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units and standards of measurement

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base quantities and derived quantities

SI Base Units Behind Measured Quantities

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conversion of units

Unit Conversion Steps and Real-World Errors

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accuracy and precision

Repeated Measurements in Science

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random and systematic errors

How Measurement Errors Affect Results

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic. Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next. A simple...

rules for significant figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

significant figures in calculations

Rounding Rules for Significant Figures

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements. The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of...

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key terms and concepts

Learn how ruler and caliper precision affects measurements and how to count significant figures from the first measured digit to the uncertain last digit.

Measurement Precision and Significant Figures | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Measurement Precision and Significant Figures

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