Write the numbers in scientific notation 673.5 = 6.735 x 10^2 0.735 x 10^2 0.034 x 10^b 0.034 x 10^b 3.4 x 10^-2
The Correct Answer and Explanation is:
To write a number in scientific notation, we express it as the product of two factors: a number between 1 and 10 multiplied by a power of 10. This is especially useful for representing very large or very small numbers concisely.
Let’s evaluate the given numbers and identify the correct scientific notations:
- 673.5 = 6.735 × 10² — This is already correctly written. The decimal point was moved two places to the left, turning 673.5 into 6.735. Since we moved the point left, the exponent is positive 2.
- 0.034 = 3.4 × 10⁻² — This is also correct. To express 0.034 as a number between 1 and 10, we shift the decimal two places to the right, turning it into 3.4. Because the decimal was moved to the right, the exponent becomes negative. Thus, b = –2.
Now, let’s review the incorrect choices:
- 0.735 × 10²: The base number is not between 1 and 10, so this is not in proper scientific notation.
- 0.034 × 10^b: If left like this, b must be positive for the product to equal 0.034, but that would contradict the rule about base numbers being between 1 and 10. So, this is an incomplete or misleading form.
- 3.4 × 10⁻² is the proper expression for 0.034 and aligns with the definition.
Scientific notation not only simplifies numbers but also helps in comparing magnitudes quickly. It is widely used in science and engineering to handle values like the mass of a cell or the distance between stars. Accuracy in this format is critical since the exponent directly affects the scale of the number.
In summary, 673.5 = 6.735 × 10² and 0.034 = 3.4 × 10⁻², with b = –2 being the correct exponent.
