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

Números significativos também ajudam a alcançar a certeza nas operações matemáticas. Além disso ou subtrair, o resultado deve ser arredondado para ter o mesmo número de casas decimais que a medida com o menor número de casas decimais.
O arredondamento por defeito deve ser realizado quando o último dígito estiver abaixo de 5 e o arredondamento por defeito for realizado quando for 5 ou superior. Outros métodos de arredondamento às vezes são usados quando o último dígito é 5.
Por exemplo, a soma de 2,052 e 1,2 é arredondada para 3,3.
No entanto, ao multiplicar ou dividir, o resultado deve ser arredondado para ter o mesmo número de algarismos significativos que a medida com o menor número de algarismos significativos. Assim, o produto de 2,052 e 1,2 é arredondado para 2,5.

algarismos significativos em cálculos

A incerteza nas medições pode ser evitada ao se relatar os resultados de um cálculo com o número correto de algarismos significativos. Isso pode ser determinado pelas seguintes regras para arredondar números:

<ol>
	<li>Ao somar ou subtrair números, arredonde o resultado para o mesmo número de casas decimais que o número com o menor número de casas decimais.</li>
	<li> Ao multiplicar ou dividir números, arredonde o resultado para o mesmo número de dígitos que o número com o menor número de algarismos significativos.</li>
	<li>Se o dígito a ser descartado (aquele imediatamente à direita do dígito que será mantido) for menor que 5, "arredonde para baixo" e mantenha o dígito mantido inalterado.</li>
	<li>Se o dígito a ser descartado (aquele imediatamente à direita do dígito que será mantido) for 5 ou maior, "arredonde para cima" e aumente o dígito mantido em 1. Métodos de arredondamento alternativos também podem ser usados se o dígito descartado for 5. O dígito mantido é arredondado para cima ou para baixo, de forma que o valor resultante seja um valor par.</li>
</ol>

Uma observação importante é que o arredondamento dos algarismos significativos deve ser preferencialmente feito no final de um cálculo de múltiplas etapas, para evitar a acumulação de erros em cada etapa devido ao arredondamento. Assim, os algarismos significativos e o arredondamento facilitam a representação correta da certeza dos valores medidos relatados.

Este texto foi adaptado 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>.

Algarismos Significativos em Cálculos

A incerteza nas medições pode ser evitada relatando os resultados de um cálculo com o número correto de algarismos significativos. Isso pode ser ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Units, Dimensions, and Measurements

Unidades, Dimensões e Medidas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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...

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

physics

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Life Science

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Texas Essential Knowledge and Skills

High School

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The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
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Reliability and Validity

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ES.1.d

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• read and interpret topographic and basic geologic maps and globes, including location by latitude and longitude

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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