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

Önemli rakamlar matematiksel işlemlerde de kesinlik elde etmeye yardımcı olur. Toplama veya çıkarma işlemlerinde, sonuç, en az ondalık basamağa sahip ölçümle aynı sayıda ondalık basamağa sahip olacak şekilde yuvarlanmalıdır.
Aşağı yuvarlama, son basamak 5'in altında olduğunda, yukarı yuvarlama ise 5 veya üzerinde olduğunda yapılmalıdır. Diğer yuvarlama yöntemleri bazen son rakam 5 olduğunda kullanılır.
Örneğin, 2,052 ve 1,2'nin toplamı 3,3 olarak yuvarlanır.
Bununla birlikte, çarpma veya bölme yapılırken, sonuç, en az anlamlı rakama sahip ölçümle aynı sayıda anlamlı rakama sahip olacak şekilde yuvarlanmalıdır. Böylece, 2,052 ve 1,2'nin çarpımı 2,5 olarak yuvarlanır.

hesaplamalarda anlamlı rakamlar

Ölçümlerdeki belirsizlik, hesaplamanın sonuçlarının uygun sayıda anlamlı rakamla raporlanarak önlenir. Rakamların yuvarlanması için aşağıdaki kurallarla belirlenebilir:

<ol>
	<li>Rakamları toplarken veya çıkartırken, sonucu noktadan sonra en az sayıda ondalık basamağı olan sayının aynı ondalık basamağına yuvarlayın.</li>
	<li>Rakamları çarptığınız veya böldüğünüzde, sonucu en az anlamlı rakama sahip sayının aynı sayıda haneli yuvarlayın.</li>
	<li>Bırakılacak rakam (korunacak rakamın hemen sağındaki rakam) 5'ten küçükse, "aşağı yuvarlayın" ve korunan rakamı değiştirmeyin.</li>
	<li>Bırakılacak rakam (korunacak rakamın hemen sağındaki rakam) 5 veya daha büyükse, "yukarı yuvarlayın" ve korunan rakamı 1 artırın. Bırakılan rakam 5 ise, alternatif yuvarlama yöntemleri de kullanılabilir. Korunan rakam, yuvarlayarak yukarı veya aşağı yuvarlanır ve sonuç çift bir değer verirse, önceki yöntem kullanılır.</li>
</ol>

Önemli bir not, anlamlı rakamların yuvarlanmasının olabildiğince çok adımlı bir hesaplama sonunda yapılması, yuvarlamadan kaynaklanan hataların her adımda birikmesini önlemek için tercih edilmelidir. Böylece, anlamlı rakamlar ve yuvarlama, rapor edilen ölçülen değerlerin kesinliğinin doğru şekilde temsil edilmesine katkıda bulunur.

Bu metin, <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'dan</a> uyarlanmıştır.

Hesaplamalarda Anlamlı Rakamlar

Ölçümlerdeki belirsizlik, bir hesaplamanın sonuçlarının doğru sayıda anlamlı rakamla raporlanmasıyla önlenebilir. Bu olabilir ...

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Units, Dimensions, and Measurements

Birimler, Boyutlar ve Ölçümler

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

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

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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

JoVE Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

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Texas Essential Knowledge and Skills

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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
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ES.1.e

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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
• 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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