Help with simple introductory problems

[Dazed]

Since my other post was ignored, I'm reposting a greatly summarized, simplified version.

Can someone teach me the basics of working with significant numbers?

Here's the 2 example problems I'm working on.

Display the answer to the correct number of significant digits.

1. 142.47 + 30.2

2. 342 x 12

To read the problems I'm having and my attempts at the solutions, see this thread: https://www.physicsforums.com/showthread.php?t=135362

A quick, non-specific, crash course in layman's terms would be most helpful.

Thanks.

 

[OlderDan]

Since my other post was ignored, I'm reposting a greatly summarized, simplified version.

Can someone teach me the basics of working with significant numbers?

Here's the 2 example problems I'm working on.

Display the answer to the correct number of significant digits.

1. 142.47 + 30.2

2. 342 x 12

To read the problems I'm having and my attempts at the solutions, see this thread: https://www.physicsforums.com/showthread.php?t=135362

A quick, non-specific, crash course in layman's terms would be most helpful.

Thanks.

When a scientist writes a number like 142.47, s/he means the number is somewhere between 142.465 and 142.475. In other words, it is some number that when rounded off to two decimal places it would be 142.47. In most cases, if the number were known more precisely more digits would have been used to represent the number. But even if it were known more precisely, when it was written as 142.47 that additional precision was lost.

Try the following and then get back to us. What are the largest and smallest results you could get in your problems if you assumed each of the numbers were as big or as small as they could be based on the digits written?

 

[Dazed]

1. 142.47 + 30.2

The smallest it could be would be..
142.465 + 30.15 = 172.615

The largest:
142.475 + 30.25 = 172.725

Right so far?

 

[OlderDan]

1. 142.47 + 30.2

The smallest it could be would be..
142.465 + 30.15 = 172.615

The largest:
142.475 + 30.25 = 172.725

Right so far?

Yes. So all you know for sure is that the sum is somewhere between 172.615 and 172.725. The midpoint between these numbers is 172.67, but that could be off by as much as 0.55 one way or the other. How many digits do you think you should used to represent the result so that it does not mislead someone into thinking you know the result more accurately than you do?

Do the same thing with the multiplication problem.

 

[Dazed]

I'm not sure, that was part of my question. I guess I want to go with the LEAST accurate (fewest decimal places) so that would be 1 decimals right? (30.2)

So my answer will have 1 decimal places.

Knowing that, I do 142.47 + 30.2 = 172.6

Is that right?

 

[Dazed]

I hope you're not getting frustrated, I just want you to understand, that I really want to make sure I understand everything, so I can do well on the tests. These assignments mean nothing they're just preparation for the tests... I want to have an intimate understanding of what I'm doing.. not just robotically repeating steps I've seen.

Your response provided me with an understanding of the purpose of significant digits. So thank you for that. I hope I can trouble you for some more knowledge yet. ;)

 

[OlderDan]

I hope you're not getting frustrated, I just want you to understand, that I really want to make sure I understand everything, so I can do well on the tests. These assignments mean nothing they're just preparation for the tests... I want to have an intimate understanding of what I'm doing.. not just robotically repeating steps I've seen.

Your response provided me with an understanding of the purpose of significant digits. So thank you for that. I hope I can trouble you for some more knowledge yet. ;)

I'm not frustrated- just not keeping up with several trains of thought. Your previous response is good. It makes no sense to keep decimal places to the right the highest, least significant digit when adding or subtracting. So you should discard the digits to the right of the position of the 2 in 30.2, or all digits to the right of the tenths place. However, you should round off other numbers to this position before you add or subtract so you should state the result as 172.7

When you multiply you will find the difference between maximum and minimum possible results much bigger than when adding or subtracting. The rule in that case is to keep only the number of digits of the factor that had the least. Your answer for 342 X 12 should have only two signifcant digits. Work out the maximum and mimimum products and see if this makes sense to you.

For adding and subtracting, it's the position of the significant digits that determines how many you keep. The number with the least significant digit at the highest place value (most to the left) is in control. For multiplying or dividing you go by the fewest number of significant digits you have in any factor.