Name: rounding rules for significant figures
Uploaded: 2023-04-30T12:12:11.000Z
Duration: 58 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Earth Science

ES.1

ES.1.c

Significant Figures in Calculations

Auch bei mathematischen Operationen tragen signifikante Zahlen zur Sicherheit bei. Bei Addition oder Subtraktion sollte das Ergebnis gerundet werden, um die gleiche Anzahl von Dezimalstellen wie die Messung mit den wenigsten Dezimalstellen zu erhalten.
Das Abrunden sollte durchgeführt werden, wenn die letzte Ziffer unter 5 liegt, und das Aufrunden, wenn sie 5 oder höher ist. Andere Rundungsmethoden werden manchmal verwendet, wenn die letzte Ziffer 5 ist.
Zum Beispiel wird die Summe aus 2,052 und 1,2 zu 3,3 gerundet.
Beim Multiplizieren oder Dividieren sollte das Ergebnis jedoch gerundet werden, um die gleiche Anzahl signifikanter Stellen zu erhalten wie die Messung mit den wenigsten signifikanten Zahlen. Somit wird das Produkt aus 2,052 und 1,2 auf 2,5 gerundet.

signifikante zahlen in berechnungen

Messunsicherheiten können vermieden werden, indem die Ergebnisse einer Berechnung mit der richtigen Anzahl an signifikanten Zahlen angegeben werden. Dies kann durch die folgenden Regeln zur Rundung von Zahlen bestimmt werden:

<ol>
	<li>Bei Addition oder Subtraktion von Zahlen wird das Ergebnis auf die gleiche Anzahl von Dezimalstellen gerundet wie die Zahl mit der geringsten Anzahl von Dezimalstellen.</li>
	<li>Bei Multiplikation oder Division von Zahlen wird das Ergebnis auf die gleiche Anzahl von Ziffern gerundet wie die Zahl mit der geringsten Anzahl von signifikanten Stellen.</li>
	<li>Wenn die zu streichende Ziffer (die unmittelbar rechts von der zu behaltenden Ziffer) kleiner als 5 ist, wird "abgerundet" und die beizubehaltende Ziffer unverändert gelassen.</li>
	<li>Wenn die zu streichende Ziffer (die unmittelbar rechts von der zu behaltenden Ziffer) 5 oder größer ist, wird "aufgerundet" und die beizubehaltende Ziffer um 1 erhöht. Ist die zu streichende Ziffer 5, können auch andere Rundungsmethoden verwendet werden. Die beizubehaltende Ziffer wird auf- oder abgerundet, je nachdem, was einen geraden Wert ergibt.</li>
</ol>

Wichtig ist zu beachten, dass die Rundung von signifikanten Zahlen idealerweise am Ende einer mehrstufigen Berechnung durchgeführt werden sollte, um die Ansammlung von Fehlern bei jedem Schritt durch Rundung zu vermeiden. Somit ermöglichen signifikante Zahlen und Rundung die korrekte Darstellung der Genauigkeit der gemessenen Werte.

Dieser Text wurde angepasst von <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, Abschnitt 1.5: Measurement Uncertainty, Accuracy, and Precision</a>.

Signifikante Zahlen in Berechnungen

Unsicherheiten bei Messungen können vermieden werden, indem die Ergebnisse einer Berechnung mit der richtigen Anzahl signifikanter Kennzahlen gemeldet werden. Dies kann ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Units, Dimensions, and Measurements

Einheiten, Dimensionen und Messungen

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 significant figures as the number with the fewest significant figures.

The digit to be dropped also matters. If that digit is less than 5, round down and keep the retained digit the same. If it is 5 or greater, round up and increase the retained digit by 1.

An alternative method may be used when the dropped digit is 5. In that case, the retained digit is rounded up or down, whichever gives an even value. In multistep calculations, rounding should preferably be done at the end. This helps avoid extra error from rounding at each step.

Rounding Rules for Significant Figures

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rules for significant figures

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significant figures in calculations

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 to round significant figures in addition, subtraction, multiplication, and division, and why rounding at the end helps reduce error.

Rounding Rules for Significant Figures | JoVE K12

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Life Science

LS.1

LS.1.b

LS.1.c

Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.2.C.

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ES.1.d

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• construct and interpret scales, diagrams, classification charts, graphs, tables, imagery, models, including geologic cross sections and topographic profiles
• read and interpret topographic and basic geologic maps and globes, including location by latitude and longitude

ES.1.e

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• compare, integrate, and evaluate sources of information presented in different media or formats to address a scientific question or solve a problem
• gather, read, and evaluate scientific and/or technical information from multiple sources, assessing the evidence and credibility of each source
• communicate scientific and/or technical information about phenomena and/or a design process in multiple formats

ES.1.f

Rounding Rules for Significant Figures

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