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Sabtu, 01 Juni 2013

An Ounce to a Kilogram Conversion

Converting an ounce to a kilogram is a good example of how to convert English measurements to SI units. As this article explains, the problem utilizes unit multipliers, metric prefixes and dimensional analysis.

Unit Multipliers

    The important thing to remember when learning about and using unit multipliers is that any number, variable or quantity multiplied by 1 is that same number, variable or quantity. In other words, multiplying by 1 does not change our original measurement.

    To create our unit multipliers for this problem, we must first know how many ounces are in a gram. This fact can be found in most physics and chemistry textbooks, as well as on the Internet.

    1 oz. = 28.35 g

    Next, we divide by one side of the equation.

    1 oz. / 1 oz. = 28.35 g / 1 oz.
    Remember anything divided by itself is 1.

    1 oz. / 1 oz. = 1 = 28.35 g / 1 oz

    If 28.35 g / 1 oz. = 1, we can multiply anything by this fraction without changing the value of our original measurement. Therefore, 28.35 g / 1 oz. is our unit multiplier.

Metric Prefixes

    To create a unit multiplier for the conversion of grams to kilograms, we must know that the prefix "kilo-" means 1,000. A kilogram is 1,000 grams.

    1,000 g = 1 kg

    1,000 g / 1,000 g = 1 kg / 1,000 g

    1,000 g / 1,000 g = 1 = 1 kg / 1,000 g

    Our unit multiplier is 1 kg / 1,000 g.

Dimensional Analysis

    Dimensional analysis is a lot easier than it sounds. Simply arrange the unit multipliers in such a way that all the units cancel (units in the numerator cancel units in the denominator) except the unit you want (in our case, kilograms).

    1 oz. (28.35 g / 1 oz.) (1 kg / 1,000 g)

Finding the Answer

    Now multiply the numbers in the numerator, multiply the numbers in the denominator and divide the numerator by the denominator.

    1 oz. (28.35 g / 1 oz.) (1 kg / 1,000 g) = 0.02835 kg

    Using our unit multipliers, we have multiplied 1 oz. by 1 twice to convert it to 0.02835 kg.

    1 oz. = 0.02835 kg

    If a problem asked how many kilograms are in 2 oz, we would multiply 2 oz by 1 twice.

    2 oz (28.35 g / 1 oz) (1 kg / 1000 g) = 0.05670 kg

    2 oz = 0.05670 kg

Other Conversions

    Using this method, you can convert pounds to kilograms, pounds to milligrams, yards to centimeters, gallons to liters, almost any unit to any other unit.

    Make sure that the units measure the same quantity (length, mass, volume, density, force or electric charge). Converting pounds to meters would be converting mass to length, and such a problem would be nonsensical.

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