This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Kuhusu jibu la swali lililopita (swali la 3 la "APPROXIMATION AND ERRORS"), nilisahau kuzungusha jibu kwa sehemu moja ya desimali kama ilivyoombwa. Jibu sahihi lilipaswa kuwa: Asilimia ya kosa la juu zaidi linalowezekana katika eneo ni 0.9\%. Sasa, hebu tutatue swali la pili kutoka sehemu ya "APPROXIMATION AND ERRORS": "Find the percentage error in using 0.47 as an estimate of (4)/(9)." Step 1: Pata thamani halisi ya (4)/(9). (4)/(9) = 0.4444... Step 2: Kokotoa kosa kamili (absolute error). Kosa kamili ni tofauti kamili kati ya thamani iliyokadiriwa na thamani halisi. Kosa kamili = |0.47 - (4)/(9)| Ili kurahisisha hesabu, tunabadilisha 0.47 kuwa sehemu: 0.47 = (47)/(100). Kosa kamili = |(47)/(100) - (4)/(9)| Pata kigawo cha kawaida cha 100 na 9, ambacho ni 900. Kosa kamili = |(47 × 9)/(100 × 9) - (4 × 100)/(9 × 100)| Kosa kamili = |(423)/(900) - (400)/(900)| Kosa kamili = |(23)/(900)| = (23)/(900) Step 3: Kokotoa asilimia ya kosa (percentage error). Asilimia ya kosa = Kosa kamiliThamani halisi × 100\% Asilimia ya kosa = (23)/(900)(4)/(9) × 100\% Ili kurahisisha, tunazidisha na kinyume cha sehemu ya chini: Asilimia ya kosa = (23)/(900) × (9)/(4) × 100\% Asilimia ya kosa = (23 × 9)/(900 × 4) × 100\% Gawanya 900 kwa 9: Asilimia ya kosa = (23 × 1)/(100 × 4) × 100\% Asilimia ya kosa = (23)/(400) × 100\% Asilimia ya kosa = (23)/(4)\% Asilimia ya kosa = 5.75\% Asilimia ya kosa ni 5.75\%. Drop the next question.