Understanding Significant Figures in Math

[Caldus]

I'm a little confused about significant figures. It is my understanding that if when you add or subtract two numbers that the result should have as many decimal places as the term with the least amount of decimal places. For example:

1.55 + 2.666 + 20.23 = 24.446 -> 24.45

Since 1.55 and 20.23 are both terms that have the least amount of decimal places, the answer should have two decimal places. Correct?

And for this one:

15.15 - 1.45 = 13.7 -> 13.70

Is this correct?

Thanks.

 

[Chi Meson]

You are correct sir!

 

[Dorita]

Yes that is correct, but you can leave out the 0 at the end of 13.7. When you Multiply or divide your answer should have the same amount of sig figs as the as the term with the least amount of Sig Figs.

ex 137.123 x 1556.1234 = 213380.309 not 213380.3089

 

[Doc Al]

Yes that is correct, but you can leave out the 0 at the end of 13.7.

No you can't--not if you wish to convey the correct number of significant figures.

When you Multiply or divide your answer should have the same amount of sig figs as the as the term with the least amount of Sig Figs.

Right.

ex 137.123 x 1556.1234 = 213380.309 not 213380.3089

Since the first number only has 6 significant figures, the answer will only have 6 significant figures: 213380.

 

[HallsofIvy]

"It is my understanding that if when you add or subtract two numbers that the result should have as many decimal places as the term with the least amount of decimal places."
No. If you do any operation on two numbers (addition, subtraction, multiplication, division) then the number of significant figures in the answer is the same as the lesser of the number of significant figures in the two numbers. "Significant figures" is not necessarily the same as "decimal places".

 

[Chi Meson]

Halls of Ivy:

I truly think that you are mistaken on this one. What you say is in direct ciontrast to every texbook that I have looked in. It also does not make sense. The rules for adding and subtracting are indeed different from the rules of multiplication and division.

If I have a single very precise distance measureing device and I measure two lengths of metal rods, the first one being 12.347 cm long and the second one being 0.025 cm long, I know the precision of each rod down to the thousandth of a centimeter. If I put these two rods together, I still have a sum that will be precises down to the thousandth of a centimeter. Why would the sum all of a sudden lose precision? Why would the sum be stated as 12 cm becaus the second measurement only has two sig figs?

I ask you to look into this. My already great respect for your knowledge will shoot up if you either conceed this point, or explain why the entire teaching establishment is wrong on this point.

 

[HallsofIvy]

Okay, I conceed the point! (I may have been thinking of multiplying numbers, but I'm not going to assert that it would be true even then!)

 

[HallsofIvy]

Okay, I concede the point! (I may have been thinking of multiplying numbers, but I'm not going to assert that it would be true even then!)

 

[Doc Al]

Chi Meson is correct. The rules for calculating the number of significant figures in the result of an arithmetic operation are different for addition/subtraction vs. multiplication/division. For addition and subtraction, it is the number of decimal places that counts.

Consider this example: 5439 m + 0.1 m = ? The second number has only 1 significant figure, so the answer is 5000 m ? Of course not! The answer is 5439 m.

Here's a reference: http://en.wikipedia.org/wiki/Significant_figures

 

[Chi Meson]

Phew! I would hate to think that I have been teaching the wrong thing to hundreds of students!

 

[HallsofIvy]

Hey, I do that all the time!

 

[Doc Al]

Hey, I do that all the time!

The students will get over it. I did. (eventually)