Question

Which of the following is the correct expression, in scientific notation, of the number 37,500 ? \( 3.75 \times 10^{3} \) \( 3.75 \times 10^{-3} \) 37,500 \( 3.75 \times 10^{4} \)

Answer 1

In scientific notation, a number is expressed as the product of a coefficient and a power of 10. For the given number 37,500, the correct scientific notation is
`\( 3.75 * 10^(4) \)`. The coefficient is 3.75, and the exponent represents the number of decimal places the original number must be moved to the left to obtain a value between 1 and 10. In this case, it is moved four places to the left, resulting in
`\( 3.75 * 10^(4) \)`.

Step-by-step explanation:

In scientific notation, a number is expressed as the product of a coefficient and a power of 10. For the given number 37,500, the correct scientific notation is
`\(3.75 * 10^(4)\)`. The coefficient, 3.75, is derived by taking the original number's non-zero digits, and the exponent, 4, represents the number of decimal places the original number must be moved to the left to obtain a value between 1 and 10. In this case, starting from 37,500, we move the decimal point four places to the left to obtain 3.75, and the resulting expression is
`\(3.75 * 10^(4)\)`.

Scientific notation is advantageous in simplifying the representation of large or small numbers, making them more manageable for calculations and comparisons. It is commonly used in scientific and mathematical disciplines, especially when dealing with measurements, astronomy, and other fields where a wide range of magnitudes is encountered. This notation is particularly convenient for expressing values in a standardized and concise manner, facilitating clearer communication of numerical information across different contexts.

Answer 2

The correct expression, in scientific notation, of the number 37,500 is 3.75 × 10^4.

Step-by-step explanation:

The correct expression, in scientific notation, of the number 37,500 is 3.75 × 104.

In scientific notation, a number is written as a decimal greater than or equal to 1 and less than 10, multiplied by a power of 10. To convert 37,500 to scientific notation, we divide it by 10 until we get a decimal between 1 and 10. We can divide 37,500 by 10 four times to get 3.75. To maintain the value of the original number, we then multiply by 104. Therefore, the correct expression is 3.75 × 104.