Associated Topics || Dr. Math Home || Search Dr. Math

### Rounding 389.512 to Three Significant Digits

```Date: 05/24/2003 at 11:23:29
From: Sunney
Subject: Rounding 389.512 to the 3 significant digits

Round 389.512 to 3 significant digits.

If we have a question like "rounding 389.512 to 2 significant
digits," we will have an answer 390. What to do with 389.512 ?
```

```
Date: 05/24/2003 at 23:25:02
From: Doctor Peterson
Subject: Re: Rounding 389.512 to the 3 significant digits

Hi, Sunney.

There is a common confusion about numbers like 390. Judging only by
the written number, you can't tell whether it is intended to have two
or three significant digits! That is because the 0 could be there
either just to hold the 3 and the 9 in the right places (and therefore
insignificant in itself), or to indicate that there are no ones in the
number (making the zero significant).

When you rounded to two significant digits, you made the number 390
with two significant digits, because the 0 is the result of rounding
and does not mean that you know the actual value in that place. But
when you rounded to three significant digits, you got 390 with three
significant digits, because this time the 0 means something. So
although the answers look the same, they mean different things, and
each is correct as an answer to its question.

To put it another way, 390 is on the one hand

the closest multiple of 10 to 389.512

and on the other hand

the closest whole number to 389.512

So whether you round to tens (2 significant digits) or to ones (3
significant digits), you get the same answer, but with a slightly
different meaning. Don't let it confuse you that they look the same.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Place Value
Elementary Terms & Units of Measurement
Middle School Terms/Units of Measurement

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search