How Many Significant Digits?Date: 10/17/2001 at 19:05:03 From: phil schwendenman Subject: Significant digits 5030 three significant digits 5030. four significant digits I still think it's three but my teacher insists that this number has four. Can you help us? Thanks, Phil Date: 10/17/2001 at 22:31:35 From: Doctor Peterson Subject: Re: Significant digits I think you are saying that your teacher says that 5030 has three significant digits, while 5030. has four. I agree with your teacher, though I'd rather not have to. Really, a number written like 5030 has ambiguous precision, since it isn't clear whether the last zero is there to represent an actual digit, or just as a placeholder. We can fix up this case by following the rule that, if the units digit is significant, we will always include the decimal point following it; therefore, it can be presumed that in 5030 the zero in the units place is not significant, while in 5030. it is. Therefore, your teacher is right. However, this rule is not sufficient to handle all cases. In 5300, we can tell that the last zero is not signficant, but what about the first zero? This could have either two or three significant digits. The only way to eliminate ambiguity is to use scientific notation: 5.3 * 10^3 has two, 5.30 * 10^3 has three, and 5.300 * 10^3 has four. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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