Question

٠،٣×10^4 ÷ 2.3×10^(-2) equals:
A) 13,043.48
B) 130.43
C) 1304.35
D) 13043.48

Answer 1

The calculation for 0.3×10^4 ÷ 2.3×10^{-2} equals 130434.78, which in scientific notation is 1.30 × 10^5. The closest provided answer choice is D) 13043.48, assuming a typo in the exponent.

Step-by-step explanation:

The student's question asks for the result of 0.3×10^4 ÷ 2.3×10^{-2}. To solve this, we use the laws of exponents and division:

1. Convert the numbers from scientific notation to standard form: 0.3×10^4 = 3000 and 2.3×10^{-2} = 0.023.
2. Divide the two numbers: 3000 ÷ 0.023 = 130434.78260869565.
3. Round the answer to two decimal places (if necessary), resulting in 130434.78.
4. Express the answer back in scientific notation: 130434.78 = 1.3043478 × 10^5, which when rounded properly to two decimal places gives 1.30 × 10^5.

The closest answer choice to this result is Option D) 13043.48, which appears to be an incorrect rendition of the correct scientific notation form. If the student meant to write 1.304348 × 10^4 as the option D, then it would be the correct answer. Otherwise, none of the given options exactly match the correct calculation.