Kendal Orenstein

**Rutger's University**

M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

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On the right of the Land of Significance, we have typically in the right of the United States, we have the Atlantic Ocean. Here we're going to talk about the Atlantic Ocean starts with an A, and we're going to say if the decimal is absent. We're going to start on the right hand side. On the left hand side, it's typically the Pacific Ocean, so we're going to use that side if the decimal is present.

What the heck am I talking about? So to understand this scenario that I've put in front of us, let's actually use some practice. So let's say I threw a number at you, and it was 200. I would like you to tell me how many significant figures it has.

Well, does 200 have a decimal place? No. So you are going to sail from the right hand side where the decimal place is absent. So we're going to put this in the Land of Significance. We're going to sail until we hit a non-zero. Once you hit a non-zero, everything to the left of that is significant. So this is significant. The 0's, not significant. So this 200 has one sig fig; and that's the 2.

How could I write that just using sig figs? Instead of writing 200, so I'm going to say 200 does not equal

200 anymore. Equals 2×10² . Then this is going to have units. Let's say it was grams. 2×10² g. Not 2.0×10²g,

because we do not want include those insignificant numbers. The only significant number in this is the 2. This

is another way we can write it.

Let's practice with another one. So let's say we have 207650cm. How many sig figs does that have in it? Well, again decimal place is absent so we're going to sail to the right until we hit a non-zero. So we're going to sail till we hit the 5. This 0 is insignificant. All of these numbers are significant. This is insignificant. Even though that there's a 0 there, it doesn't mean that it's not significant. So we have 1, 2, 3, 4, 5, 6 figs. Again, another way to write this is to say 2.0765×10 to the 4cm. This is our answer. Notice I did include the decimal places in this one because, they are all significant, but not the last zero.

So let's say the decimal place is present. Let's say it's there, we do have a decimal place. So let's say we do have the number. I'm going to say the number 2.700g. This time we're going to sail from the left hand side until we hit a non-zero. Same thing; sail and we hit a non-zero immediately. All of these numbers are significant. Which means we have 4 sig figs. So that's actually fine.

Let's say I give you another number 0.0720mL. Do the same thing. We're going to sail from the left, sail, sail, sail, we hit the non-zero here. These numbers are just place-holders, and not necessary. All these are significant. So we have 3 sig figs. If I were to represent this just using sig figs, I would again but using scientific notation, say 7.20, including that 0 because it is significant, times 10 to the -2 milliliters here. So this would be our practice number just using sig figs.

So actually instead of memorizing all those rules that you see sometimes in textbook, and you see sometimes when your teacher explains what a sig fig is, that can get a bit overwhelming, and a bit cumbersome. So this method is actually really easy, and it's fail-proof. It will never let you, and you can use this method every time when you're counting sig figs. This is will help you to get the correct answer when you're doing calculation. I hope this helped.