Name: counting significant figures in measurements
Uploaded: 2023-09-22T11:49:39.000Z
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 figuren

Rules of Significant Figures

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 Figuren

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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counting significant figures in measurements

Significant figures help students record measurements with the correct level of precision. They show which digits in a number are meaningful and which only help place the decimal point. In science class, this idea matters when writing and comparing measured values.

The rules for significant figures explain how to count these digits in different numbers. Some digits are always counted, while others depend on where they appear in the number. Learning the rules makes it easier to report answers clearly and consistently.

This topic is especially useful in physics and other measurement-based science work. It helps students decide how many digits to keep when writing results from lab work or calculations. That makes numerical answers easier to interpret and compare.

Counting Significant Figures in Measurements

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Learn how to count significant figures in measurements and report scientific values with the right precision for high school science and lab work.

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Counting Significant Figures in Measurements

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