# How many sig figs do i use when making conversions

1. Aug 31, 2008

### kevinlikesphysics

1. The problem statement, all variables and given/known data

I have to do a bunch of problems such as converting meter to km and cups to mililiters etc. How do i calculate sig figures for these problems

for example

i did 12 miles to kilometers

12 miles x 1.609 km/1mile = 19.308 km = 19 km ? do i leave the sig figs at 19.308 or do i change the answer to 19 to make the answer only 2 signigicant figures? because 12 miles is only 12 sig figs i made the answer two is that correct....thanks

2. Relevant equations

3. The attempt at a solution

2. Aug 31, 2008

### symbolipoint

How many significant figures in your final result depends on the the starting accuracy of your information. In your case, you began with two figures, "12". You should keep TWO significant figures for your result, in your case, "19 km".

3. Aug 31, 2008

### kevinlikesphysics

awesome thanks ....so the conversion ratio doesnt apply at all in these cases then right?

4. Aug 31, 2008

### symbolipoint

The conversion factor definitely applies. The limitation on significant figures depends on which number has the smallest amount of significant figures in the conversion expression. In your case, your 12 miles is what restricts you to two signif. figure. Your conversion factor has plenty of figures.
....in fact your conversion factor would limit you to FIVE significant figures; but since your number to convert only has TWO sigfigs, you are limited to two significant figures.

5. Aug 31, 2008

### Redbelly98

Staff Emeritus
Note that some conversion factors are exact by definition, and can be considered to have an infinite number of significant figures.

Examples:
1 cm = 0.01 m
1 foot = 12 inches
1 inch = 2.54 cm

6. Sep 1, 2008

### Staff: Mentor

Could be my English fails me, but this sounds ambiguous to me. Is it 12 miles as measured (in which case it has 2 significant digits) or is it exactly 12 miles (12 is an integer, in which case it has infinite number of SD)?

7. Sep 1, 2008

### HallsofIvy

Staff Emeritus
I would interpret that as having two significant figures.

8. Sep 1, 2008

### Redbelly98

Staff Emeritus
I agree, "12 miles" has 2 sig figs. I can't imagine a situation, in real life, where you would know something is exactly 12 miles.

9. Sep 1, 2008

### Staff: Mentor

12 miles is exactly 12 miles

Note, that HallsofIvy to some extent confirmed ambiguity writing "I would interpret". I would interpret the question the same way most likely, assuming it is 2 SD. But it is just an interpretation.

Question doesn't state whether it asks about the real world measurements, or about abstract conversion factors. I can easily imagine student that interprets 12 as an exact number and gives 19.312128 km as an answer. Not accepting this answer when the exact meaning of the question is open to interpretation will be IMHO wrong.

If the question would say something like "I have measured distance between my home and school to be 12 miles, how far it is in km", that'll be completely different story.

10. Sep 2, 2008

### chemisttree

One might have been given the problem of determining how many miles were in 10,560 fathoms...

In that case the number of sig figs is not 2.