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

Znaczące cyfry pomagają również osiągnąć pewność w operacjach matematycznych. Dodawanie lub odejmowanie wynik należy zaokrąglić w dół, aby mieć taką samą liczbę miejsc dziesiętnych, jak pomiar z najmniejszą liczbą miejsc dziesiętnych.
Zaokrąglanie w dół powinno być wykonywane, gdy ostatnia cyfra jest poniżej 5, a zaokrąglanie w górę, gdy wynosi 5 lub więcej. Inne metody zaokrąglania są czasami używane, gdy ostatnią cyfrą jest 5.
Na przykład suma 2,052 i 1,2 jest zaokrąglana do 3,3.
Jednak podczas mnożenia lub dzielenia wynik należy zaokrąglić, aby uzyskać taką samą liczbę cyfr znaczących, jak pomiar z najmniejszą liczbą cyfr znaczących. W związku z tym iloczyn liczb 2,052 i 1,2 zaokrągla się do wartości 2,5.

znaczące liczby w obliczeniach

Niepewności pomiarów można uniknąć, podając wyniki obliczeń z odpowiednią liczbą cyfr znaczących. Można to określić na podstawie następujących zasad zaokrąglania liczb:

<ol>
	<li>Podczas dodawania lub odejmowania liczb zaokrąglij wynik do tej samej liczby miejsc po przecinku, co liczba z najmniejszą liczbą miejsc po przecinku.</li>
	<li>Podczas mnożenia lub dzielenia liczb zaokrąglij wynik do tej samej liczby cyfr, co liczba z najmniejszą liczbą cyfr znaczących.</li>
	<li>Jeśli cyfra, która ma zostać usunięta (ta bezpośrednio na prawo od cyfry, która ma zostać zachowana) jest mniejsza niż 5, zaokrąglij w dół i pozostaw pozostawioną cyfrę bez zmian.</li>
	<li>Jeśli cyfra, która ma zostać usunięta (ta bezpośrednio na prawo od cyfry, która ma zostać zachowana) wynosi 5 lub więcej, zaokrąglij w górę i zwiększ pozostawioną cyfrę o 1. Alternatywa można również zastosować metody zaokrąglania, jeśli opuszczona cyfra wynosi 5. Zachowana cyfra jest zaokrąglana w górę lub w dół, w zależności od tego, która wartość daje wartość parzystą.</li>
</ol>

Ważną informacją jest to, że zaokrąglanie cyfr znaczących najlepiej wykonywać na końcu obliczeń wieloetapowych, aby uniknąć kumulacji błędów na każdym kroku w wyniku zaokrągleń. Zatem cyfry znaczące i zaokrąglenia ułatwiają prawidłowe przedstawienie pewności zgłaszanych wartości pomiarowych.

Ten tekst jest adaptacją <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemistry 2e, sekcja 1.5: Niepewność pomiaru, dokładność i precyzja</a>.

Znaczące liczby w obliczeniach

Niepewności pomiarów można uniknąć, podając wyniki obliczeń z prawidłową liczbą cyfr znaczących. To może być ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Units, Dimensions, and Measurements

Jednostki, wymiary i pomiary

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

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models, theories, and laws

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units and standards of measurement

SI Units for Physical Quantities

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estimation of the physical quantities

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accuracy and precision

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random and systematic errors

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rules for significant figures

Measurement Precision and Significant Figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

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

Dimensional Checks in Physics Equations

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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

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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• ask questions that arise from careful observation of phenomena, examination of a model or theory, or unexpected results, and/or to seek additional information
• determine which questions can be investigated within the scope of the school laboratory or field experience
• generate hypotheses based on research and scientific principles
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• construct and revise explanations based on valid and reliable evidence obtained from a variety of sources, including students' own investigations, models, theories, simulations, and peer review
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ES.1.d

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• evaluate the merits and limitations of models
• develop, revise, and/or use models based on evidence to illustrate or predict relationships
• 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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The student will demonstrate an understanding of scientific and engineering practices by obtaining, evaluating, and communicating information
• 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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