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OlderDan

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I stongly believe that all conversions should be taught as multiplication of a given quantity by the identity, 1. There are countless ways to write 1 as the ratio of any two equals. For example to convert feet to inches

[tex] 3 feet = 3 feet * \frac{12 inches}{1 foot} = 36 inches[/tex]

This can be extended to changes of measuring systems

[tex] 3 feet = 3 feet * \frac{12 inches}{1 foot} * \frac{2.54 cm}{1 inch} = 91.44 cm[/tex]

All conversions can be done by multiplying by appropriate representations of 1. One should never have to think about when to divide and when to multiply. The units tell us which way to form the numerator and denominator of the fraction equal to 1.

[tex] 3 feet = 3 feet * \frac{12 inches}{1 foot} = 36 inches[/tex]

This can be extended to changes of measuring systems

[tex] 3 feet = 3 feet * \frac{12 inches}{1 foot} * \frac{2.54 cm}{1 inch} = 91.44 cm[/tex]

All conversions can be done by multiplying by appropriate representations of 1. One should never have to think about when to divide and when to multiply. The units tell us which way to form the numerator and denominator of the fraction equal to 1.

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OlderDan

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2.54 cm = 1 inch

1 mile = 5280 feet

1 liter = 1000 cm^3

etc etc etc

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OlderDan

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mass = density * volume

For water density = 1 gm/cm^3

mass of water = (1gm/cm^3)*volume of water

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