Significant digits in our conversation

This has 2 significant digits, this has 3.

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.

I'll just round it three significant digits, 7.67 meters per second

Gives me .72 I'll just round to two significant digits 0.72

Let's see if we can learn a thing or two about significant figures, sometimes called significant digits.

In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits.

So if you saw something like this, you would say 3 significant digits.

So in this situation every digit the way it's written is a significant digit. So you have six significant digits.

And this makes it very clear that we only have 2 significant digits here.

And it looks like I had 2 significant digits in each of these original things,

I had 1.0 over here, not 100 clear how many significant digits I have over here.

We get 7670 7671, but I'll just stick to three significant digits, 7670 meters per second

y year with 2 digits Y year with 4 digits m month with 1 or 2 digits M month with 2 digits d day with 1 or 2 digits D day with 2 digits H hours with 2 digits I minutes with 2 digits S seconds with 2 digits

Although, instead of an infinite number of sixes, we're limited by the number of significant digits available.

Digits

Digits

I'll assume that it's rounded to the nearest 10 kilometers, so we only have 2 significant digits here.

Fract digits

Group digits

4 Digits

Single digits.

So we should only have 2 significant digits in our answer, so we're gonna round this to 78 m s.

So let's write this over here so, any non zero digits and zero's in between are going to be significant.

A better way to show that you've measured to 3 significant digits would be to write it in scientific notation.

Number one, if you haven't noticed, you should notice that results estimates are only accurate to about three significant digits.

And that let's you know that there was actually five digits of precision that we actually go to five significant figures.

We saw in the last video that when you multiply or you divide numbers, or (I guess I should say when you multiply or divide measurements) your result can only have as many significant digits as the thing with the smallest significant digits you ended up multiplying and dividing.

Minimum number of digits

Maximum number of digits

Whether to group digits

Whether to group digits.

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.

let's see if we can come up with some rules of thumb for figuring out how many significant figures, or how many significant digits, there are in a number or a measurement.

So I have 260 times 1000 divided by 3600 gets me, I'll just round it to 72, because that's about how many significant digits

So the first thing that is pretty obvious is that any non zero digit, and any of the zero digits in between are significant.

Maximum number of digits displayed

Number of fixed decimal digits

Maximum number of digits displayed.

Number of fixed decimal digits.

Let's add up these digits.

I forget all the digits.

let's go to four digits.

So just as a quick example, if I have 2.00 times (I don't know) 3.5 my answer over here can only have 2 significant digits

2 times 3.5 is 7, and we can get to 1 zero to the right of the decimal. Because we can have 2 significant digits.