// Numbas version: exam_results_page_options {"name": "Numbastest uke 34: St\u00f8rrelser", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], []], "questions": [{"name": "Gjeldende siffer 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Hvor mange gjeldende siffer har følgende tall

", "advice": "

Når vi skal regne gjeldende siffer så teller vi alltid fra og med det førstetallet som ikke er null, og til og med den siste nullen etter komma. Dette er fordi det er stor forskjell på $120,0$ og $120,000\\ 000$ i siste tilfellet har vi gjort langt, langt mer nøyaktige målinger og har en mye lavere usikkerhet.

a)Her har vi to siffer før komma, og fire etter, altså 6 siffertotalt.

b)Her har vi null siffer før komma, og to etter, altså 2 siffertotalt.

c)Her har vi null siffer før komma, og ett etter, altså 1 siffertotalt

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a) $-14,5400$ [[0]]

b) $-0,14\\cdot10^3$ [[1]]

c) $0,004$ [[2]]

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Du har fått tallet {a} som resultat av en måling, men vurdering av usikerheten tilsier at du bare har grunnlag for å oppgi svaret med bestemte antall gjeldende siffer.

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Skriv svaret med {b} gjeldende siffer (husk at det må skrives punktum, f.eks. 3.5 ikke 3,5)

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Skriv svaret med {c} gjeldende siffer (husk at det må skrives punktum, f.eks. 3.5 ikke 3,5)

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Sidene i et rektangulært svømmebasseng er målt i henholdsvis {a} meter og {b} meter med usikkerhet. Finn arealet av vannoverflaten, fornuftig avrundet.

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Når vi skal regne med enheter er en fin huskeregel at vi alltid skal ta med like mange gjeldende siffer som det tallet med færrest gjeldende siffer. I dette tilfellet skal vi altså ha med to gjeldende siffer. Merk at når vi gjør selve utregningen tar vi med alle sifferene, og gjør avrundingen til sist slik at vi unngår avrundingsfeil.

$A={\\var{a}}\\cdot{\\var{b}}=\\simplify{{a*b}}$

Arealet av omkretsen til bassenget er altså {c} meter.

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Husk at det må skrives punktum, f.eks. 3.5 ikke 3,5

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De varmhvite lysene, som vi har ofte som myk, koselig innendørs belysning i hjemmet er på cirka 2500 Kelvin

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Hva er måltall, benevning og enhet?

En stoff har massetetthet $\\var{a}$ g / $cm^3$, det vil si $\\var{a}$ gram per kubikkcentimeter.

", "advice": "

La oss først bytte til enheter til. Siden $1\\mathrm{cm} = 10^{-2}\\mathrm{m}$ får vi

$\\dfrac{\\var{a}\\mathrm{g}}{\\mathrm{cm}^3}=\\dfrac{\\var{a}\\mathrm{g}}{(10^{-2}\\mathrm{m})^3}=\\dfrac{\\var{a}\\mathrm{g}}{10^{-6}\\mathrm{m}^3}=\\var{a}\\cdot10^{6}\\mathrm{g}\\ \\mathrm{m}^{-3}$

Altså veier $\\var{b}\\mathrm{m}$ av dette stoffet $\\var{a}\\cdot\\var{b}\\cdot 10^{6}\\mathrm{g}=\\simplify{{a*b}}\\cdot 10^{6} \\mathrm{g}$ eller $\\simplify{{a*b}}\\cdot 10^{3}\\ \\mathrm{kg}$ eller $\\simplify{{a*b}}\\ \\mathrm{tons}$

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$\\var{b} m^3$ av dette stoffet veier

[[0]] gram

[[1]] kilogram

[[2]] tons

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SI-prefikser er prefikser som kan anvendes sammen med enhetene i SI-systemetfor å danne avledede enheter som er av en annen størrelsesorden enn grunnenheten

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Velg et riktig prefiks for hver tipotens

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Hver $\\mathrm{cm}^2$ av Jordens overflate bærer en luftsøyle med masse 1 kg. Jordens overflate er $5,1\\cdot 10^8\\ \\mathrm{km}^2$.

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a) En metode er å regne om $5,1\\cdot 10^8\\ \\mathrm{km}$ til $\\mathrm{cm}^2$. Siden $1 \\mathrm{km}=10^3\\ \\mathrm{m}=10^5 \\mathrm{cm}$ får vi $5,1\\cdot 10^8\\ \\mathrm{km}^2=5,1\\cdot 10^8\\cdot(10^5\\ \\mathrm{cm})^2=5,1\\cdot 10^{8+5\\cdot 2}\\ \\mathrm{cm}^2=5,1\\cdot 10^{18}\\ \\mathrm{cm}^2$

Atmosfæren sin masse er altså ca $5,1\\cdot 10^{18}$ kg

b) Nå trenger vi å regne ut 22% av svaret fra oppgave a). Siden% betyr hundrededdel så får vi

$5,1\\cdot 10^{18}\\cdot0,22\\ \\mathrm{kg}=1,122\\cdot 10^{18}$ kg

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Finn atmosfærens masse i kg

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22% av atmosærens masse er oksygen. Finn massen av oksygenet i atmosfæren.

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La følgene benevnte størrelser være gitt

$a_1=\\var{a}\\mathrm{m}^{\\frac{\\var{b}}{2}}\\mathrm{s}^{\\frac{\\var{c}}{3}}$

$a_2=\\var{d}\\mathrm{m}^{\\frac{\\var{f}}{2}}\\mathrm{s}^{\\frac{\\var{g}}{3}}$

og la $a$ være den benevnte avledede størrelsen

$a=a_1^{\\var{g}}\\cdot a_2^{\\var{b}}$

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Måltallet til $a$ er $\\langle a\\rangle$=[[0]]

Benevningen til $a$ er $[a]=\\mathrm{m}$ ^ [[1]] $\\mathrm{s}$ ^ [[2]]

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