if the zeroes of 0.000005 is not significant then might as well throw em all in the trash and put it as 5
So, 0.000005 is = 5 which is obviously wrong
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Can someone explain to me what perspective I need to understand them? And also why my mindset is wrong
In: Mathematics
To understand significant figures, you have to understand the problem it’s solving.
We often talk about real-world measurements in science, like “I added 450 milliliters of distilled water”.
The problem is that you might have been off in that measurement. You probably used a measuring beaker that had lines that you visually judge, you might have gotten a little bit above or below the line. The measuring line itself is almost a millimeter thick, even if you hit the line exactly you still might be in the bottom or top part of the line instead of dead center. Plus a few drops stuck to the bottom and sides when you poured it out. Plus there might have been slight differences in the size of the beaker and the placement of the marks in the manufacturing process that created it.
All this stuff is the *error* in the measurement, how much you think the measurement would be off by.
In real scientific calculations you often talk about this error using a separate term, like this: 450 mL ± 3 mL. That means you think your measurement might have been off by up to 3 mL in either direction.
Significant figures solve the following problem: *If you have a number that doesn’t explicitly tell you the error, how much error should you assume it has?*
If I tell you it’s 2000 miles from New York to Los Angeles, it’s pretty clear that’s not very accurate. Based on that statement, the actual distance could be anywhere from 1500 to 2500 miles.
On the other hand, if I tell you a track is 2.00 meters long, how long do you think it could actually be? I didn’t need to include those extra zeros after the decimal point, the only reason I included them is to tell you that I’m confident it’s between 1.99 and 2.01 meters.
If I’m doing some experiment and I tell you the laser spot moved 0.005 meters, you’ll be wildly wrong if you convert that measurement to 5 meters. What I meant is that it’s between 0.0045 and 0.0055 meters long, but I can’t measure anything smaller than a millimeter. If I was using some more accurate measuring device / technique that gave me tenths of millimeters, I’d say it was 0.0050 meters long.
*Significant figures of a number shouldn’t change based on your measurement units* so 0.005 meters has one significant figure regardless of whether we choose to talk about it as 0.005m or 5 mm or 5000 micrometers.
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