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### 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/
```
Associated Topics:
Elementary Fractions
Elementary Place Value

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