To find the number of meters in six kilometers, why do you multiply 6*10 to the power of 3?

Our conversion factor is: 1km = 1000m; 1000m is 10^3m. Since there are more meters in kilometers, we can't divide but multiply. We have 6km times the amount of meters in 1km = 1000m or 10^3m. That is why 6*10^3 = 6000m which is 6km in meters.

Another way of looking at this is;

There's 1000m in 1km (so we use it as a conversion factor).  We multiply 6 * 1000 and divide by 1.

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