What is the number of significant figures in each of the...

What is the number of significant figures in each of the following measurements?
(a) 4867 mi
(b) 56 mL
(c) 60,104 tons
(d) 2900 g
(e) $40.2 \mathrm{~g} / \mathrm{cm}^3$
(f) 0.0000003 cm
(g) 0.7 min
(h) $4.6 \times 10^{19}$ atoms

Transcript

00:01 Hi.

00:02 So this question is asking to look at these measurements and just say how many significant digits there are in each one of them so let's just get started this first part a here we have 4 ,867 miles so for sig figs anything that isn't zero is definitely a significant digit zero is the only kind of tricky one but everything else like one two three five six seven eight nine ten or three five seven eight nine are all definitely significant so here we all have no zeros, so we know that all four of these are indeed significant.

00:36 So we have four sigpics here.

00:38 So look at the next one, 56 milliliters, kind of the same thing, no zeros.

00:42 So both of these are significant.

00:44 So two sigpigs.

00:46 Now this next one, see, 60 ,104 tons.

00:50 Now we have some zeros here, but zeros are counted significant only a couple scenarios.

00:54 They're counted when they are sandwiched by significant digits.

01:01 So yeah, if there's significant digits on both sides of it or several zeros that are encompassed by significant digits, then they are significant.

01:11 So as you can see here, both of these zeros are sandwiched by significant digits.

01:16 We have the first one is sandwiched by six and one, and second one sandwiched by one and four.

01:19 So all of those zeros and all the other digits are significant.

01:23 So every single number in this number here is significant.

01:27 So it's five figs.

01:29 Now the next one.

01:31 2 ,900 grams.

01:34 Now this is a scenario in which the zeros actually are not significant.

01:38 Now as you can see, these zeros, they are one side, they have a significant digit, right? they have a 9.

01:45 On the left side, or on the right side, there are no significant digits here.

01:49 So both of these zeros are insignificant and 2 and 9 are still significant because they're not zero.

01:54 So we have two sig -figs here.

01:58 Now for e, 40 .2 grams per centimeter cubed.

02:02 Now, it's kind of similar to c, where we have a zero that is sandwiched by significant figures, 4 and 2...

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