# How do you add subtract multiply and divide significant figures

In other words, the "appropriate" number of significant digits is two, and you would report in your physics lab report, for instance that the volume of the block is 42 cubic inches, approximately. The length is 5. Introduction to Art History.

The idea is this: Suppose you measure a block of wood. The length is 5. To find the volume, you would multiply these three dimensions, to get But can you really, with a straight face, claim to have measured the volume of that block of wood to the nearest thousandth of a cubic inch?!? Each of your measurements was accurate as far as you can tell to two significant digits: So you cannot claim five decimal places of accuracy, because none of your measurements exceeded two digits of accuracy. As a result, you can only claim two significant digits in your answer.

In other words, the "appropriate" number of significant digits is two, and you would report in your physics lab report, for instance that the volume of the block is 42 cubic inches, approximately.

### Significant Digits: Additional Considerations

How do you round when they give you a bunch of numbers to add? You would add or subtract the numbers as usual, but then you would round the answer to the same decimal place as the least -accurate number.

Looking at the numbers, I see that the second number, So my answer will have to be rounded to the tenths place:. The digit in the tenths place is a 2and it's followed by another 2so I won't be rounding up. Rounding to the tenths place, I get:.

The requirement to round your answer, when adding values, to the same "place" as the largest that is, furthest to the left, with respect to the decimal point last accurate place of the input values, might make a little more sense if you view the addition vertically:.

When you look at the columns of digits, it kinda makes sense that, yeah, you can't claim any accuracy past the tenths place, because that's the last column that all the input numbers share. Looking at each of the numbers they've given me, I see that I will have to round the final answer to the nearest tens place, because is only accurate to the tens place. The other numbers are accurate to the ones, tenths, and ones places, respectively.

How do you round, when they give you numbers to multiply or divide? You would multiply or divide the numbers as usual, but then you would round the answer to the same number of significant digits as the least-accurate number. This was 3, this is 2. We only limited it to 2, because that was the smallest number of significant digits we had in all of the things that we were taking the product of. When we do addition and subtraction, it's a little bit different. And I'll do an example first.

I just do a kind of a numerical example first, and then I'll think of a little bit more of a real world example. And obviously even my real world examples aren't really real world. In my last video, I talked about laying down carpet and someone rightfully pointed out,"Hey, if you are laying down carpet, you always want to round up. Just because you don't wanna it's easier to cut carpet away, then somehow glue carpet there.

But that's particular to carpet. I was just saying a general way to think about precision in significant figures. That was only particular to carpets or tiles.

But when you add, when you add, or subtract, now these significant digits or these significant figures don't matter as much as the actual precision of the things that you are adding. How many decimal places do you go? For example, if I were to add 1. If you just add these two numbers up, and let's say these are measurements, so when you make it these are clearly 3 significant digits we're able to measure to the nearest hundreth.

Here this is two significant digits so three significant digits this is two significant digits, we are able to measure to the nearest tenth. Let me label this. This is the hundredth and this is the tenth. When you add or subtract numbers, your answer, so if you just do this, if we just add these two numbers, I get - what?

The sum, or the difference whatever you take, you don't count significant figures You don't say,"Hey, this can only have two significant figures.

The least precise thing I had over here is 2. It only went to the tenths place, so in our answer we can only go to the tenths place. So we need to round this guy up. Cause we have a six right here, so we round up so if you care about significant figures, this is going to become a 3. And I want to be clear.

This time it worked out, cause this also has 2 significant figures, this also has two significant figures. But this could have been Then, in this situation - this obviously over here has 4 significant figures, this over here has 3 significant figures. But in our answer we don't want to have 3 significant figures.

We wanna have the The least precise thing we only go one digit behind the decimal over here, so we can only go to the tenth, only one digit over the decimal there. So once again, we round it up to And to see why that makes sense, let's do a little bit of an example here with actually measuring something.

So let's say we have a block here, let's say that I have a block, we draw that block a little bit neater, and let's say we have a pretty good meter stick, and we're able to measure to the nearest centimeter, we get, it is 2. Let's say we have another block, and this is the other block right over there. We have a, let's say we have an even more precise meter stick, which can measure to the nearest millimeter. And we get this to be 1.

So measuring to the nearest millimeter. And let's say those measurements were done a long time ago, and we don't have access to measure them any more, but someone says 'How tall is it if I were stack the blue block on the top of the red block - or the orange block, or whatever that color that is? Well, if you didn't care about significant figures or precision, you would just add them up.

## Adding and Subtracting Using Significant Figures

You'd add the 1. So let me add those up: So you get 3. And the problem with this, the reason why this is a little bit You don't know, if I told you that the tower is 3.

The reality is that I was only be able to measure the part of the tower to the millimeter. This part of the tower I was able to measure to the nearest centimeter.