Question

Goal: Use dimensional analysis to solve conversion problems. 1. Observe: In the question, you are asked to convert kilometers to centimeters. To do this, first you will convert kilometers to meters. Drag the 1000 meters/1 kilometer tile down. A. What do you notice? __________________________________________________ B. Because kilometers appear in the numerator of one term and in the denominator of another, they cancel, or disappear. The process of converting units by canceling is called dimensional analysis. How many meters are in 0.828 kilometers? ________________________________ C. A meter is a much shorter unit of measurement than a kilometer. Based on this fact, does your answer to B make sense? ______________________________________

Answer 1

Answer:

A. The kilometers unit is cancelled out and the result shown is 828 meters.

B. 828 meters are found in 0.828 Kilometers

C. Yes

Explanation:

A. When the 1000 meters/1 kilometer tile is dragged down, the kilometers unit is cancelled out and the value 828 meters appears.

This is because the kilometers appear in the numerator of one term and in the denominator of another, they cancel, or disappear. The process of converting units by canceling is called dimensional analysis.

B. 0.828 Kilometers * 1000 meters/1 kilometer = 828 meters

Therefore, there are 828 meters in 0.828 kilometers.

C. A meter is a much shorter unit of measurement than a kilometer. Based on this fact, it does make sense that 0.828 Kilometers which is less than 1 kilometer is equal to 828 meters.

Answer 2

(A) The process of converting units by canceling is called dimensional analysis.

(B)  There are 828 meters in 0.828 kilometers.

(C) It does make sense that  0.828 Kilometers which is less than 1 kilometer is equal to 828 meters.

The given problem is based on some basic fundamentals and applications of dimensional analysis. So as per the given problem, each subpart says,

A.

When the 1000 meters/1 kilometer tile is dragged down, the kilometers unit is cancelled out and the value 828 meters appears.

This is because the kilometers appear in the numerator of one term and in the denominator of another, they cancel, or disappear. The process of converting units by canceling is called dimensional analysis.

Thus, we can conclude that the process of converting units by canceling is called dimensional analysis.

B.

Converting the given value of kilometers into the meters as,

0.828 Kilometers * 1000 meters/1 kilometer = 828 meters

Thus, we can conclude that there are 828 meters in 0.828 kilometers.

C.

A meter is a much shorter unit of measurement than a kilometer. Based on this fact, it does make sense that 0.828 Kilometers which is less than 1 kilometer is equal to 828 meters.

Thus, we can conclude that it does make sense that  0.828 Kilometers which is less than 1 kilometer is equal to 828 meters.

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