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
Significant figures are primarily about how *precise* your numbers are – and rounding rules for significant figures is about showing how precise the result is based on the numbers you put in. Zeroes before the significant digits simply show magnitude, and as a result are not significant.
Typically when doing measurements, the last significant digit of your measurement is considered approximate, since it’s the limit of whatever measurement technique you’re using.
So to take your example of 0.000005, let’s say it’s a measurement. If it’s by itself, the magnitude (the zeroes) are important, because it shows how large the value in question is. However, if you now have another measurement, let’s say 0.003, and you need to add the two together, significant digits would become important. Saying the result of adding the two is 0.003005 would not be correct, because it suggests a precision that you don’t have in your second measurement (since the last digit is approximate, a measured value of .003 could be .00299 or .00305 in reality) – you have to round to .003.
Another way to look at it is that if you can replace zeroes with a change in unit, then those zeroes aren’t significant. So if your measurement of 0.000005 is in grams, you can get rid of the zeroes by instead stating it as 5 micrograms.
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