Willa R. answered • 02/18/17
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Experienced, Skilled Educator & Renaissance Woman, PhD in Physics
This is a simple unit conversion problem. The conversion factor is given, albeit indirectly. If one inch is 2.5 cm, then the conversion factor is (1 inch)/(2.5 cm). We can combine this with the amount of centimeters we're actually working with, 16.6 cm, as follows
x inches = 16.6 cm * (1 inch)/(2.5 cm)
In unit conversions, it can be difficult for some students to know which part of the conversion factor goes on top--why it is (1 inch)/(2.5 cm) rather than (2.5 cm)/(1 inch). This is where checking units comes in handy. Units can cancel out by division just like numbers can, and they multiply as easily as numbers and variables. So if the cm went on top, we would have cm2/inch, which is not at all what we want. But if we have inches on top and cm on the bottom, then you get cm*inches/cm, which is just inches.
Simply carry out the division 16.6/2.5 to get the amount of inches.
x inches = 16.6 cm * (1 inch)/(2.5 cm)
In unit conversions, it can be difficult for some students to know which part of the conversion factor goes on top--why it is (1 inch)/(2.5 cm) rather than (2.5 cm)/(1 inch). This is where checking units comes in handy. Units can cancel out by division just like numbers can, and they multiply as easily as numbers and variables. So if the cm went on top, we would have cm2/inch, which is not at all what we want. But if we have inches on top and cm on the bottom, then you get cm*inches/cm, which is just inches.
Simply carry out the division 16.6/2.5 to get the amount of inches.
