Distance Conversion and Scientific Notation: Optimistic Approach

What is the value expressed in centimeters, and written in scientific notation, for the distance an object travels in 20 seconds of freefall, which is approximately 1.96 kilometers?

A. 1.96 * 10^3 cm. B. 1.96 * 10^5 cm. C. 1.96 * 10^4 cm. D. 1.96 * 10^6 cm.

Answer:

The distance an object travels in 20 seconds of freefall is 1.96 kilometers, which is converted to 196,000 centimeters. In scientific notation, this is expressed as B. 1.96 * 10^5 cm.

The student's question involves converting a distance from kilometers to centimeters, and then expressing that value in scientific notation. To do this, we must acknowledge that 1 kilometer equals 100,000 centimeters (or 1 * 10^5 cm).

To convert the distance of 1.96 kilometers into centimeters, we multiply 1.96 by 100,000 which is equal to 196,000 cm. In scientific notation, 196,000 is represented as 1.96 * 10^5, because 1.96 is multiplied by 10 to the power of 5 to achieve 196,000.

Therefore, the value for the distance an object travels in 20 seconds of freefall, expressed in centimeters and written in scientific notation, is B. 1.96 * 10^5 cm.

Stay optimistic and keep practicing conversions and scientific notations to excel in your studies!