Final answer:
To find the quotient of 7.536 * 10^7 and 7.85 * 10^2 in scientific notation, divide the decimal parts, subtract the exponents of 10, adjust the quotient to proper scientific notation form, and combine the results. The final answer is approximately 9.601274 x 10^4 or 9.60 x 10^4 if rounded to three significant figures.
Step-by-step explanation:
To calculate the quotient of 7.536 × 107 and 7.85 × 102 and express it in scientific notation, you follow these steps:
Divide the decimal parts: 7.536 / 7.85 = 0.9601274 (rounded off for simplicity)
Subtract the exponents of 10: 107 / 102 = 107-2 = 105
To express the result in scientific notation, adjust the decimal part to have one non-zero digit before the decimal point: 0.9601274 => 9.601274 × 10-1
Combine the adjusted decimal part with the result of exponent subtraction: 9.601274 × 10-1 × 105 = 9.601274 × 104
The final result in scientific notation is 9.601274 × 104. If you need to round the decimal to a certain number of significant figures, please specify how many. For example, if we round to three significant figures, the result would be 9.60 × 104.