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

Des chiffres significatifs aident également à obtenir une certitude dans les opérations mathématiques. En addition ou en soustraction, le résultat doit être arrondi pour avoir le même nombre de décimales que la mesure avec le moins de décimales.
L’arrondi à la baisse doit être effectué lorsque le dernier chiffre est inférieur à 5, et l’arrondi à la hausse lorsqu’il est supérieur ou égal à 5. D’autres méthodes d’arrondi sont parfois utilisées lorsque le dernier chiffre est 5.
Par exemple, la somme de 2,052 et 1,2 est arrondie à 3,3.
Cependant, lors de la multiplication ou de la division, le résultat doit être arrondi pour avoir le même nombre de chiffres significatifs que la mesure avec le moins de chiffres significatifs. Ainsi, le produit de 2,052 et 1,2 est arrondi à 2,5.

chiffres significatifs dans les calculs

L'incertitude dans les mesures peut être évitée en rapportant les résultats d'un calcul avec le nombre correct de chiffres significatifs. Cela peut être déterminé en suivant les règles suivantes pour l'arrondi des nombres :

<ol>
	<li>Lors de l'addition ou de la soustraction de nombres, arrondir le résultat au même nombre de décimales que le nombre ayant le moins de décimales.</li>
	<li>Lors de la multiplication ou de la division de nombres, arrondir le résultat au même nombre de chiffres que le nombre ayant le moins de chiffres significatifs.</li>
	<li>Si le chiffre à supprimer (celui immédiatement à droite du chiffre à conserver) est inférieur à 5, "arrondir à la baisse" et laisser le chiffre conservé inchangé.</li>
	<li>Si le chiffre à supprimer (celui immédiatement à droite du chiffre à conserver) est égal ou supérieur à 5, "arrondir à la hausse" et augmenter le chiffre conservé de 1. Des méthodes d'arrondi alternatives peuvent également être utilisées si le chiffre supprimé est 5. Le chiffre conservé est arrondi à la hausse ou à la baisse, selon ce qui donne une valeur paire.</li>
</ol>

Il est important de noter que l'arrondi des chiffres significatifs devrait de préférence être effectué à la fin d'un calcul à plusieurs étapes afin d'éviter l'accumulation d'erreurs à chaque étape due à l'arrondi. Ainsi, les chiffres significatifs et l'arrondi facilitent la représentation correcte de la certitude des valeurs mesurées rapportées.

Ce texte est adapté de <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision</a>.

Chiffres significatifs dans les calculs

L’incertitude dans les mesures peut être évitée en rapportant les résultats d’un calcul avec le nombre correct de chiffres significatifs. Cela peut être ...

Education

Enseignement

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Physics

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Unit 1

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Units, Dimensions, and Measurements

Unités, dimensions et mesures

KEY TERMS AND CONCEPTS

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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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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

physics

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Reliability and Validity

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ES.1.d

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ES.1.e

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The student will demonstrate an understanding of scientific and engineering practices by obtaining, evaluating, and communicating information
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Rounding Rules for Significant Figures

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