Question
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2. (a) Diberi \( g=4.3 \times 10^{3} \) dan \( h=6.54 \times 10^{4} \), hitungkan nilai \( \frac{g+h}{g h} \) Nyatakan jawapan anda dalam bentuk piawai dan betul kepada tiga angka bererti Given \( g=4.3 \times 10^{3} \) and \( h=6.54 \times 10^{4} \), calculate the value of \( \frac{g+h}{g h} \) State your answer in the standard form and correct to three significant figures Jawapan / Answer:

Ask by Herrera Todd. in Malaysia
Jan 27,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

\[ \frac{g + h}{g \cdot h} = 2.48 \times 10^{-4} \]

Solution

Given: \[ g = 4.3 \times 10^{3} \] \[ h = 6.54 \times 10^{4} \] We need to calculate: \[ \frac{g + h}{g \cdot h} \] **Step 1: Calculate \( g + h \)** \[ g + h = 4.3 \times 10^{3} + 6.54 \times 10^{4} = 4.3 \times 10^{3} + 65.4 \times 10^{3} = 69.7 \times 10^{3} = 6.97 \times 10^{4} \] **Step 2: Calculate \( g \cdot h \)** \[ g \cdot h = (4.3 \times 10^{3}) \times (6.54 \times 10^{4}) = 4.3 \times 6.54 \times 10^{7} = 28.122 \times 10^{7} = 2.8122 \times 10^{8} \] **Step 3: Compute the expression** \[ \frac{g + h}{g \cdot h} = \frac{6.97 \times 10^{4}}{2.8122 \times 10^{8}} = \frac{6.97}{2.8122} \times 10^{-4} \approx 2.48 \times 10^{-4} \] **Final Answer:** \[ \frac{g + h}{g \cdot h} = 2.48 \times 10^{-4} \]

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Untuk menghitung \( \frac{g+h}{gh} \), kita terlebih dahulu perlu menghitung nilai \( g + h \) dan \( g h \). 1. Menjumlahkan \( g \) dan \( h \): \[ g + h = 4.3 \times 10^{3} + 6.54 \times 10^{4} = 4.3 \times 10^{3} + 65.4 \times 10^{3} = 69.7 \times 10^{3} \] 2. Menghitung \( g h \): \[ g h = (4.3 \times 10^{3})(6.54 \times 10^{4}) = 4.3 \times 6.54 \times 10^{3+4} = 28.162 \times 10^{7} \] 3. Menghitung \( \frac{g+h}{g h} \): \[ \frac{g+h}{gh} = \frac{69.7 \times 10^{3}}{28.162 \times 10^{7}} \] \[ = \frac{69.7}{28.162} \times 10^{3-7} = 2.474 \times 10^{-4} \] Akhirnya, menyatakan jawapan dalam bentuk piawai dan betul kepada tiga angka bererti: \[ \text{Jawapan: } 2.47 \times 10^{-4} \]

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