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## Arithmetic (all content)

### 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? • 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. • 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 • 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? • 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?
• why do they round up so much? can someone give me conditions for when that happens? • At around he says that 350ft is measured to the tenth feet, but I don't get it. There are 3 digits, so wouldn't that be a hundredth... or could someone tell me how this works?
(1 vote) For this kind of problems, we are interested in the most accurate measurement to the right of the number. The more you go to the left, the less accurate your measurement will be. We don't focus on the measurement of the hundreds because this is the stuff we measured, in a way, before going on to measure the tens, which are more "tricky" since they require more precise instruments so as be measured.

The background:
If our number is a decimal, finding the least significant figure (useful to solve the problem) is perhaps more obvious because it's all written down, complete with trailing 0's (that are different from those you would find in the purely mathematical videos that precede this one, in that they actually inform us that the measurement was made precisely up to a certain digit).
If we're dealing with a whole number without a decimal point and without a line above or below a digit, we tend to assume that any 0's present to the right of the number are the product of rounding or insufficient accuracy, and thus not count them as significant. In 350, three hundreds and five tens are significant, but the most fine measurement is the five tens. We don't have sufficient data about the ones' place! It could theoretically be anything from 0 to 9, although if it's greater than five we would have probably measured it as 360 in the first place (except if the 5 in the tens' place becomes a 4 and we round up) .  