Write down 9.938 to two significant figures.
So in this question, we’re actually asked to write down a number to two significant figures. So what we’re gonna look at first is what counts as significant figures. Well, when we’re talking about significant figures, the first significant figure is the first nonzero digit.
So, for instance, if we had 2.3672, then the first two is our first significant figure. And if we had 0.007323, then the seven would be the first significant figure because all the digits in front are actually zeros.
So quickly look at this number. So we’ve got 3.20374. So it’s worth noting that if the zero is actually amongst the actual other digits, then it actually counts towards our significant figure. So in this case, the zero is the third significant figure. It only wouldn’t count as a significant figure if it’s before the first nonzero digit.
Okay, great! So we’ve now got all the tools we need. So now let’s actually write down 9.938 to two significant figures. Well, if we look at 9.938, we can actually see we’ve got four significant figures here. But what we want is to actually write it down as two significant figures.
Therefore, in order to do this, what I do is I put a line behind the second significant figure, so that’s this nine. And then even though it’s the nine that we’re actually gonna be dealing with, the number that’s gonna help us decide what happens next is actually the number to the right of our nine or the next place value down.
So in this case, it’s actually a three. And the key thing to notice about the three is that it’s less than five. And that’s because if this number to the right-hand side or the next place value down is actually less than five, then the value that we want, so our significant figure, will stay the same. However, if it’s five or above, we’d actually round the number up.
So therefore, as we said, because this number is a three and it’s actually lower than five, then our significant figure, the nine, is gonna stay as it is. So therefore, we can say that 9.938 to two significant figures is 9.9. And I’ve written 9.9 and then in brackets “two sf.” And that’s because “two sf” stands for two significant figures.