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

Die Sicherheit der Messung hängt von zwei Faktoren ab: der Anzahl der Ziffern bei der Messung und der Genauigkeit des verwendeten Instruments.
In einer gemessenen Größe werden alle Ziffern, einschließlich der letzten unsicheren Ziffer, als signifikante Stellen bezeichnet – und können nach bestimmten Regeln bestimmt werden.
Alle Ziffern ungleich Nullen und alle Captive-Nullen - die zwischen zwei Stellen ungleich Null liegen - sind signifikant. Zum Beispiel hat 28 zwei signifikante Zahlen, während 26,25 vier und 208 drei hat.
Führende Nullen sind nie von Bedeutung, da sie nur den Dezimalpunkt lokalisieren. Zum Beispiel hat 0,00208 drei signifikante Zahlen. Solche Größen können mit Hilfe von Exponentialnotationen ausgedrückt werden. Somit kann 0,00208 als 2,08 × 10−3 geschrieben werden.
Nachfolgende Nullen sind nur in Zahlen im Dezimalformat von Bedeutung. 2200 hat zwei nachgestellte Nullen und zwei signifikante Ziffern, während 2200.0 und 2200.1 beide 5 signifikante Ziffern haben.
Bei Größen ohne Dezimalstellen wird die Bedeutung von nachgestellten Nullen mehrdeutig. So kann 2200 als 2,2 × 103 mit zwei signifikanten Ziffern oder 2,20 x 103 mit drei signifikanten Ziffern geschrieben werden.

regeln für signifikante zahlen

Bei jeder Messung ist die Präzision des Messinstruments ein wesentlicher Faktor. Ein gewöhnliches Lineal kann beispielsweise Längen auf den nächsten Millimeter genau messen; eine Schieblehre hingegen kann Längen auf die nächsten 0,01 mm genau messen. Daher ist die Schieblehre ein präziseres Messinstrument, da sie extrem kleine Veränderungen in der Länge messen kann. Die Messungen werden genauer sein, wenn das Messinstrument präziser ist.

Es sollte betont werden, dass bei der Darstellung gemessener Werte die letzte Ziffer auf irgendeine Weise vom Messenden berechnet wurde. Zum Beispiel bemerkt eine Person, die mit einem Lineal die Länge eines Stiftes misst, dass sie zwischen 13,2 cm und 13,3 cm liegt, und daher muss sie den Wert der letzten Ziffer schätzen. Die Regel der signifikanten Ziffern besagt, dass die letzte Ziffer, die in einer Messung aufgeschrieben wird, die erste Ziffer mit einer Unsicherheit ist. Beginnen Sie mit dem ersten gemessenen Wert links und zählen Sie die Anzahl der Ziffern bis zur letzten geschriebenen Ziffer rechts, um die Anzahl der signifikanten Ziffern in einem Wert zu bestimmen. Signifikante Ziffern repräsentieren die Präzision des verwendeten Messinstruments für die Messung eines Wertes.

Dieser Text ist angepasst von<a href="https://openstax.org/books/university-physics-volume-1/pages/1-6-significant-figures"> Openstax, University Physics Volume 1, Abschnitt: 1.6 Signifikante Zahlen.</a>

Regeln für Signifikante Zahlen

Bei jeder Messung ist die Präzision des Messwerkzeugs ein wesentlicher Faktor. Ein gewöhnliches Lineal kann zum Beispiel die Länge auf die nächste ...

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Units, Dimensions, and Measurements

Einheiten, Dimensionen und Messungen

KEY TERMS AND CONCEPTS

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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

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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...

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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

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Measurement Precision and Significant Figures

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