Write the numbers in scientific notation. 673.5 673.5 = 6.735 × 10a = 67.35 Incorrect 0.034 0.034 = × 10b = Incorrect Incorrect
The Correct Answer and Explanation is:
Correct Scientific Notation:
- 673.5 = 6.735 × 10²
- 0.034 = 3.4 × 10⁻²
Explanation:
Scientific notation is a method used to express very large or very small numbers in a concise and standardized form. It is written as the product of two parts: a decimal number between 1 and 10, and a power of 10. This format looks like N × 10ⁿ, where N is the significant figure and n is the exponent indicating how many places the decimal point has been moved.
For 673.5, the decimal is moved two places to the left to get a number between 1 and 10, resulting in 6.735. Since we reduced the magnitude of the number to make it smaller, we balance that change by multiplying with 10 raised to the positive power of 2. This gives 6.735 × 10².
For 0.034, the decimal point is moved two places to the right to yield 3.4. Because the original number is smaller than 1, the exponent becomes negative to reflect this decrease in value. So, 0.034 becomes 3.4 × 10⁻².
A common mistake, like in the image you uploaded, is writing 673.5 as 67.35 × 10¹ or omitting the coefficient for 0.034 entirely. However, scientific notation requires the coefficient to fall strictly within the range of 1 to less than 10. Any violation of that rule leads to incorrect notation.
This form of expression is especially useful in science and engineering, where values often span many orders of magnitude. It provides clarity and makes calculations involving extremely large or small quantities much more manageable.
