Math CentralQuandaries & Queries


Question from Hannah:

What is the scale factor of 36 meters and 1.5 centimeters?

Hi Hannah,

First I need both sides of the scale factor to be in the same units and since there are 100 centimeters in a meter, 36 meters is 3600 centimeters. Hence the scale is 3600 centimeters to 1.5 centimeters.

I would like both of these numbers to be integers and since $2 \times 1.5 = 3$ I am going to multiply both by 2 to get a scale of 7200 centimeters to 3 centimeters. Hence the scale factor is

\[\frac{7200}{3} = \frac{2400}{1}.\]

I hope this helps,

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