Examples:  Converting Between Metric Units
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We want to perform the following conversions using the metric system. The nice thing about the metric system is it’s base-ten, so it makes conversions very convenient. The basic unit of measure for length in the metric system is the meter, volume it’s the liter, and weight it’s the gram. And then from the basic unit of measure, we have these prefixes that represent different amounts of the basic unit. For example a kilometer is one thousand meters, a killiliter is one thousand liters, and a kilogram is one thousand grams. Versus a millimeter is one thousandth of a meter, milliliter is one thousandth of a liter, and milligram is one thousandth of a gram. And we have several other
prefixes that represent different amounts of the basic unit. For the first example, we want to convert four meters to centimeters. Looking at our chart here, we can see that a centimeter is one-hundredth of a meter, which means one way to convert from
meters to centimeters is to multiply by one hundred. But one of the most convenient things about having this chart is if you identify the column of the units that you have, and the column of the units that you want to convert to, you can just count the number of columns and move your decimal that number of places in the same direction. What I mean by that is if we’re here at
meters, and we want to convert to centimeters, we want to change the units from here to here, which is two columns to the right. So we can just take the number four with the decimal place here, and move the decimal point two places to the right. One, two, which would make four meters equal to four hundred centimeters. In the next example we want to convert two point five millimeters to meters. So millimeters would be in this column here with the prefix milli. We want to convert this back to the basic unit of measure meter. And since a millimeter is one thousandth of a meter, we could just divide by one thousand, or by counting the number of columns we’re moving, from here, one, two, three columns to the left. So we can take two point five, move the decimal to the left three places. So we’d have one, two, three. We have to add a couple zeroes here, so two point five millimeters is equal to point zero, zero, two, five meters. And sometimes you’ll see text
books put a zero here in the ones column. Let’s go and take a look at two more
of these. We want to convert milliliters to killiliters. So we’re in this column for milliliters, we want to convert all the way to killiliters. So we can just take our decimal point and move it one, two, three, four, five, six places to the left. So if we start with two hundred fifty, with the decimal point here. Now we’ll move the decimal point to the left six times. One, two, three, four, five, six. So we’ll have to add three extra zeros, one, two, three, making two hundred fifty milliliters equal to point zero, zero, zero, two, five, and we can leave of this last zero. Remember any extra zeros to the right of this last digit would not change the value of the decimal. And again we want to put a zero here in the ones place value. And for the last example we want to convert one point two, five kilograms, that would be this column here, to the
basic unit of grams, here in the middle. So the shortcut would be to move the decimal point one, two, three places to the right. Or we could also just multiply by one thousand. So we have one point two, five. Move the decimal point to the right three times, one, two, three. So we have one thousand two hundred fifty grams. And just in case you’re not familiar with these abbreviations, I’ll leave you with this table here, that shows all the abbreviations for meters, liters, and grams.

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