Final answer:
The question pertains to performing operations with numbers in scientific notation. Through multiplication and division of both the coefficients and the exponents, the result is 1.5 x 10⁴ in scientific notation.
Step-by-step explanation:
The question involves the multiplication and division of numbers in scientific notation. Scientific notation is a way to express very large or very small numbers in a more compact form. The calculation: 2.54 x 10⁵ x 4.76 x 10² / 8.06 x 10³ is performed using the laws of exponents.
First, let's multiply the numbers without exponents: 2.54 x 4.76 = 12.0904. Now, we'll add the exponents for multiplication: 10⁵ x 10² gives us 10⁷ (because 5+2=7). Next, we'll divide by 8.06 and subtract exponents for division: 10⁷ / 10³ gives us 10⁴ (because 7-3=4).
The division of 12.0904 by 8.06 in decimal form is approx. 1.5. Therefore, combining this with the exponent part, we get 1.5 x 10⁴. This is our result in proper scientific notation, complies with the rules of significant figures, and is performed without the use of a calculator as per the question's requirement.