Metric Unit ConversionsDate: 08/21/2001 at 21:59:26 From: Damian Montgomery Subject: Changing metric units How do you know when you should multiply or divide in these conversions? Date: 08/22/2001 at 14:20:18 From: Doctor Ian Subject: Re: Changing metric units Hi Damian, Actually, when converting units, you're always multiplying by 1 (which is why you can do it without changing the meaning of anything). For example, 1 in 1 ft 3 cm * -------- * ------ = ? 2.54 cm 12 in ^ ^ | | This is So is this. the same as '1'. Note that you can treat the units just as if they were numbers; and since the order of multiplications is irrelevant, you can group them all at the end 1 in 1 ft 3 * 1 * 1 cm * in * ft 3 cm * -------- * ------ = --------- * -------------- 2.54 cm 12 in 2.54 * 12 cm * in Once they're grouped like that, you can cancel them, just as you would cancel numbers that appear in both the numerator and denominator of a fraction: x x 1 in 1 ft 3 * 1 * 1 cm * in * ft 3 cm * -------- * ------ = --------- * -------------- 2.54 cm 12 in 2.54 * 12 cm * in x x = 3 / (2.54 *12) ft So, when you need to convert something, how do you decide whether to multiply by 21.2 blurgs ------------- 0.015 zibbles or 0.015 zibbles ------------- ? 21.2 blurgs The answer depends on which unit you need to cancel. If you're starting with zibbles, the first one will give you zibbles * blurgs ---------------- zibbles which is the same as blurgs; but if you're starting with blurgs, then the second one will give you blurgs * zibbles ---------------- blurgs which is the same as zibbles. Does this help? Let me know if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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