4. (a) How many significant figures are contained in the...

4. (a) How many significant figures are contained in the following numbers: (i) 2020 (ii) 0.3010 (iii) 3.050 (iv) 1.10 \times 10^{-2} (v) 1.10 \times 10^{2} (b) Evaluate the expressions below, and express your answer with the correct number of significant figures. Also, state the number of significant figures in your answer. (i) 1.1 + 0.11 (ii) 1.1 - 0.11 (iii) 1.1 \times 0.11 (iv) 1.1 \div 0.11 (v) 11 + 2 \times 10 - 2.4 \div 2^{3}

Transcript

00:01 So this question involves figure out how many significant figures are each of these numbers.

00:08 So for the first part of the question, we have 243.

00:12 All these are non -zero digits.

00:14 So all of these numbers are going to be significant.

00:17 So we have three significant figures.

00:20 Next, 7 ,063 .1.

00:25 All of these numbers are significant.

00:28 If a zero is between two non -zero numbers, it is significant.

00:33 And then any number to the right of a decimal point is significant.

00:37 So this one has a total of one, two, three, four, five, so five significant figures.

00:43 Next, we go to 2 .7.

00:47 Because these zeros are to the right of the decimal point, then they're all significant.

00:56 So all of these digits in this number are significant, which we have five, so we have five significant figures.

01:02 Next, we have 5 .98 times 10 to negative 3.

01:05 This is scientific notation.

01:08 We just look at these numbers here when we're determining significant figures.

01:12 They're all non -zero, so they're all significant.

01:15 So we have three significant figures.

01:17 Next, we have 2 ,430.

01:21 So this might differ on your textbook.

01:25 This zero at the end is kind of called the ambiguous zero.

01:29 If there was a decimal point here, then we would know for.

01:32 Sure that the zero was significant.

01:35 But because there is no decimal point, we don't know if it's significant or not.

01:40 So we're going to say that it's not significant, and then we're just going to include these first three digits.

01:46 So we'll say it has three significant figures.

01:49 Next, we have 0 .0251.

01:52 Now the only numbers, if you have a zero directly, like the first number after the decimal point, it is not significant.

02:00 Only the numbers to the right of that zero, are significant.

02:04 So the only significant figures are going to be these.

02:07 So we have three significant figures.

02:10 Now we have just the number three.

02:13 It's a non -zero number.

02:14 We only have one digit, so we have one significant figure.

02:18 Next, we have 1 .010 times 10 of the fourth.

02:21 Again, this is scientific notation, so we're only paying attention to these digits here.

02:26 Because this zero is between two non -zero digits...

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