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.
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Question 8: Evaluate 3/(2.125 × 0.064) without using Mathematical Tables or Calculators. Step 1: Badilisha nambari za desimali kuwa sehemu rahisi. Kwanza, badilisha nambari za desimali katika denominator kuwa sehemu: 2.125 = (2125)/(1000) Gawanya nambari na denominator kwa 125: 2.125 = (2125 ÷ 125)/(1000 ÷ 125) = (17)/(8) Pili, badilisha nambari ya pili ya desimali kuwa sehemu: 0.064 = (64)/(1000) Step 2: Rahisisha denominator. Sasa zidisha sehemu hizi mbili: 2.125 × 0.064 = (17)/(8) × (64)/(1000) Futa 8 kutoka kwa 64: = (17 × (8 × 8))/(8 × 1000) = (17 × 8)/(1000) = (136)/(1000) Step 3: Badilisha thamani iliyorahisishwa kwenye usemi wa mzizi wa tatu. Sasa weka denominator iliyorahisishwa kwenye usemi wa asili: 3/(136)1000 Ili kugawanya kwa sehemu, zidisha kwa kinyume chake: = 3/(136) = 3/(136) Step 4: Rahisisha sehemu ndani ya mzizi wa tatu. Gawanya nambari na denominator kwa kigawanyo chao kikubwa zaidi. Tunaweza kugawanya zote mbili kwa 8: 93000 = 93 × 1000 = 93 × 125 × 8 136 = 17 × 8 Hivyo, sehemu inakuwa: (93 × 125 × 8)/(17 × 8) = (93 × 125)/(17) Step 5: Kokotoa mzizi wa tatu. Sasa usemi ni: 3/(17) Tunajua kwamba 125 = 5^3, kwa hivyo [3]125 = 5. = 3/(17) × 125 = 3/(17) × [3]125 = 3/(17) × 5 = 5 3/(17) Thamani ya usemi ni: 5 3/(17) Drop the next question.