Which of the following is the correct way to write the value 50000 expressed in scientific
The Correct Answer and Explanation is:
The correct answer is 5.0 × 10⁴.
Scientific notation is a way of writing numbers that makes them easier to work with, especially for extremely large or small values. This notation consists of two parts: a coefficient and a power of ten. The coefficient is a number between 1 and 10, and the exponent on the power of ten represents how many times the coefficient must be multiplied by ten to obtain the original number.
To express 50000 in scientific notation, consider the significant digits requirement. The number 50000 has two significant digits: 5 and 0. To convert this number into scientific notation while maintaining exactly two significant digits, it is necessary to rewrite it in the form of a coefficient multiplied by a power of ten.
Start by placing the decimal point after the first significant digit, which is 5, yielding 5.0. The number of places the decimal point is moved determines the exponent of ten. In this case, shifting the decimal point four places to the left results in the correct exponent, 4. This operation confirms that 50000 can be rewritten as 5.0 × 10⁴.
Examining the answer choices, 50.0 × 10³ and 50 × 10³ are incorrect because the coefficient exceeds the acceptable range of values between 1 and 10. The option 5.00 × 10⁴ contains three significant digits rather than two, making it an inaccurate representation based on the given requirement.
Thus, the scientifically accurate way to write 50000 with two significant digits is 5.0 × 10⁴, ensuring the number retains precision while maintaining the appropriate notation format. This approach allows for efficient calculations and clear numerical representation in scientific and engineering contexts.
