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### Course: Arithmetic (all content)>Unit 6

Lesson 14: Significant figures

# Addition and subtraction with significant figures

This video teaches addition and subtraction with significant figures, emphasizing that the result should match the least precise measurement. It offers examples and explains the real-world importance of maintaining precision in calculations. Created by Sal Khan.

## Want to join the conversation?

• Wouldn't 3.56 be rounded to the nearest tenth be 3.6 and not 3.7? Is that a mistake?
• yeah its a mistake... no problem though it is supposed to be 3.6 so..
• Shouldn't 103.56 be rounded to 103 and not 103.6 since 3 significant figures is less than four as Sal did?
• No, because with addition (and subtraction) it isn't the significant figures that matter. In fact, this video isn't at all about significant figures. It's about decimal places (d.p). 1.26 went to 2 d.p. Whereas 102.3 only went to 1 d.p. As 1 d.p is less than 2 d.p. The answer can only go to 1 d.p.

As you can see, significant figures don't come into it at all, and with the title, I can see why this would be confusing.
• Hi, i have a couple of questions for my physics course concerning Sig digits:
1) what about when doing complicated math stuff, like squaring a number, or when adding two numbers and then taking the square root, or when using SIN COS or TAN, and so on. how many sig figs do we use then?
(2 What if there are multiple steps in the math problem. what if i have to find the distance and time of a movement, and then using those values find the velocity. do i round the significant digits at the end or do i round each one.
• Im not so sure about your first question, and I would like to know the answer as well, but answering your second question, you should always round the answer at the end. It easier to do this and it's less likely to make a mistake :)
• in the last example how was it that 350 had the least amount of significant figures compared to 8. 8 has less digits
• 350 has the same amount of significant digits as 8.8, actually. Did you mean 8.08?

In significant digits you often have to figure out how many significant digits somebody else's number has. We have rules for doing this. If we didn't have rules, we wouldn't know anything. We wouldn't know whether 350 had an estimating digit of 5 or 0 or 3 or what. That's why we have significant digit rules that all people are supposed to follow. By these rules; the estimating digit of 350 is 5. So, it has two significant digits. 8.08 has an estimating digit of 8 (in the hundredth place), so it has three significant digits. Make sense?
• In what order does one round?
For example,
(2.526/3.1)+(0.470/0.623)+(80.725/0.04326)= ?
Would I add together each quotient and then round (128.1272741 ; what sig fig place would I round to?)
, or would I round each quotient, add them together, and then round again (188.11)?
Much thanks
• So rounding Significant Figures work in the order of PEMDAS as well?
• So, according to what Sal said near the end of the video,
10 + 1 = 10?
This doesn't seem right to me.
• Why not call the tower on the building 358 but put a line either above or below the 10's digit to show precision only to within 10 feet?
• Sal has mentioned a in multiple videos that this would be acceptable, but it is a style that is not commonly used. Scientific notation would be the preferred method if you truly want to show what level of precision was used.
(1 vote)
• why is 102.3 the least significant numb in the problem when it has 4 significant figures?