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

Cifre significative aiutano a raggiungere la certezza anche nelle operazioni matematiche. In addizione o sottrazione, il risultato deve essere arrotondato per avere lo stesso numero di cifre decimali della misura con il minor numero di cifre decimali.
L'arrotondamento per difetto deve essere eseguito quando l'ultima cifra è inferiore a 5 e l'arrotondamento per eccesso deve essere eseguito quando è pari o superiore a 5. Altri metodi di arrotondamento vengono talvolta utilizzati quando l'ultima cifra è 5.
Ad esempio, la somma di 2,052 e 1,2 viene arrotondata a 3,3.
Tuttavia, durante la moltiplicazione o la divisione, il risultato deve essere arrotondato per avere lo stesso numero di cifre significative della misurazione con il minor numero di cifre significative. Pertanto, il prodotto di 2,052 e 1,2 viene arrotondato come 2,5.

cifre significative nei calcoli

L'incertezza nelle misurazioni può essere evitata dal riportare i risultati dei calcoli con il numero corretto di cifre significative. Questo può essere determinato dalle seguenti regole per arrotondare i numeri:

<ol>
	<li>Quando si addizionano o sottraggono i numeri, arrotondare il risultato allo stesso numero di cifre decimali del numero con il minor numero di cifre decimali.</li>
	<li>Quando si moltiplicano o dividono i numeri, arrotondare il risultato allo stesso numero di cifre del numero con il minor numero di cifre significative.</li>
	<li>Se la cifra da eliminare (quella immediatamente a destra della cifra da mantenere) è inferiore a 5, “arrotondare per eccesso” e aumentare la cifra mantenuta di 1. Metodi alternativi di arrotondamento possono essere usati anche se la cifra eliminata è 5. La cifra mantenuta viene arrotondata per eccesso o per difetto, a seconda di quale produca un valore pari.</li>
</ol>

Un'osservazione importante è che l'arrotondamento delle cifre significative dovrebbe essere preferibilmente fatto alla fine di un calcolo multifase per evitare l'accumulazione di errori causato dall'arrotondamento ad ogni passo. Pertanto, le cifre significative e gli arrotondamenti facilitano la corretta rappresentazione della certezza dei valori misurati riportati.

Questo testo è adattato da <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>

Cifre significative nei calcoli

L'incertezza nelle misurazioni può essere evitata riportando i risultati di un calcolo con il numero corretto di cifre significative. Questo può essere ...

Education

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Physics

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Unit 1

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Units, Dimensions, and Measurements

Unità, dimensioni e misurazioni

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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...

dimensional analysis

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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

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Texas Essential Knowledge and Skills

High School

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• make quantitative and/or qualitative claims based on data
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• 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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