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

Significant figures help achieve certainty in mathematical operations, too. In addition or subtraction, the result should be rounded off to have the same number of decimal places as the measurement with the fewest decimal places.
Rounding down should be performed when the last digit is below 5, and rounding up carried out when it is 5 or above. Other rounding methods are sometimes used when the last digit is 5.
For instance, the sum of 2.052 and 1.2 is rounded off as 3.3.
However, while multiplying or dividing, the result should be rounded to have the same number of significant figures as the measurement with the fewest significant figures. Thus, the product of 2.052 and 1.2 is rounded off as 2.5.

significante cijfers in berekeningen

Onzekerheid in metingen kan worden vermeden door de resultaten van een berekening met het juiste aantal significante cijfers te rapporteren. Dit kunt u bepalen aan de hand van de volgende regels voor het afronden van getallen: <ol> <li>Wanneer u getallen optelt of aftrekt, rondt u het resultaat af op hetzelfde aantal decimalen als het getal met het minste aantal decimalen.</li> <li>Wanneer u getallen vermenigvuldigt of deelt, rondt u het resultaat af op hetzelfde aantal cijfers als het getal met het minste aantal significante cijfers.</li> <li>Als het cijfer dat moet worden weggelaten (het cijfer direct rechts van het cijfer dat moet worden behouden) kleiner is dan 5, "naar beneden afronden" en laat het behouden cijfer ongewijzigd.</li> <li>Als het cijfer dat moet worden weggelaten (dat direct rechts van het cijfer dat moet worden behouden) een 5 of hoger is, "naar boven afronden" en het behouden cijfer met 1 verhogen. Alternatief Afrondingsmethoden kunnen ook worden gebruikt als het weggelaten cijfer 5 is. Het behouden cijfer wordt naar boven of naar beneden afgerond, afhankelijk van wat een even waarde oplevert.</li> </ol> Een belangrijke opmerking is dat het afronden van significante cijfers bij voorkeur moet gebeuren aan het einde van een meerstapsberekening om de accumulatie van fouten bij elke stap als gevolg van afronding te voorkomen. Significante cijfers en afrondingen vergemakkelijken dus een correcte weergave van de zekerheid van de gerapporteerde gemeten waarden. Deze tekst is overgenomen uit <a href="https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision">Openstax, Chemie 2e, Sectie 1.5: Meetonzekerheid, nauwkeurigheid en precisie</a>.

Significante cijfers in berekeningen

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be ...

Education

JoVE Core

Physics

Natuurkunde

Unit 1

Onderdeel 1

Units, Dimensions, and Measurements

Eenheden, dimensies en metingen

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

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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units and standards of measurement

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base quantities and derived quantities

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accuracy and precision

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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...

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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

Specialised Topic in Science

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ES.1.d

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• 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

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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
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Rounding Rules for Significant Figures

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