 Let's do some examples. Pause the video and try these for yourself. How many sig figs are in each of these numbers? Okay. 102.87. This starts with a non-zero digit, the 1, and goes on from there. The only zero in it is a captive zero, which we know is significant. So this number has 1, 2, 3, 4, 5 sig figs. Okay. 45,000. This number starts with two significant figures, the 4 and the 5, but these are followed by three trailing zeros. Since there's no decimal point in this number, they're non-significant because we don't know if those zeros are exact or the result of rounding off. So this number just has two sig figs. 0.020. This number starts with two leading zeros, which are not significant. We start counting when we get to the first non-zero digit, that's the 2, and the trailing zero is significant this time because the number has a decimal point. So two sig figs here. 0.009050. This is much like the last one. Start counting the sig figs at the 9, which is the first non-zero digit, and that gives us four sig figs in total. Okay, last example. This number is written in scientific notation rather than standard notation. So let's rewrite it in standard notation. It equals 0.0415. And you should be able to see now that it has three sig figs because the first two zeros aren't significant. Now look back at the scientific notation. Notice that when the number is written as 4.15 times 10 to the minus 2, those three significant figures are placed in obvious fashion at the start of the number. The non-significant zeros are hidden. Instead of having them there as placeholders, we're using the times 10 to the minus 2 part to give the digits their correct place value instead. And this leads me to a useful tip. If you're ever in doubt about sig figs, convert to scientific notation. Scientific notation gets rid of non-significant digits. The first part of the number shows you all the sig figs, and the second part just adjusts the place values. This also gives us a strategy for dealing with the ambiguity in numbers like 45,000. What if we actually want to write 45,000 to five sig figs? That is, we want to show that the 45,000 was measured accurately to the nearest whole number. Well, if we write it in scientific notation, we can show that those zeros are significant by including them in the first part of the notation. When written like this, the trailing zeros become part of a number with a decimal point, and so we know for sure that they are significant. So brush up on your scientific notation. Now I'm just going to revisit this example for a second because there's a potential misunderstanding here that I want to clear up. Just because the leading zeros are not significant doesn't mean they disappear. 0.020 is not the same as 20. You can't get rid of those first two zeros. The function of those first two zeros is as placeholders for the place value. They say there are no ones and there are no tenths. The actual useful part of the measurement starts at the two in the hundredths place and goes on with the final zero. These are the digits that tell us the size of the number. But if we don't have those first two zeros, then the two would have the wrong place value, and that would muck everything up.