AB Yes? Good.

Because we can have 2 significant digits.

This is the thousandths place.

So our final answer can only the 3 significant figures.

So between the leading digit and the decimal sign.

So let's do seven hundred let me switch colors.

By contrast, your place of birth is more likely to include letters rather than numbers.

Just give some indication if it's right.

Times seven hundred ninety eight.

Well, I'll write it like this.

It's a threedigit code.

Another three digit (Applause)

AB Yes?

Let's do five hundred twenty three times

But we go from a nine, eight, seven, six, five on this digit, on the second digit.

But, before we begin, we're going to try another little magic trick.

Seven? Seven?

I have 4 significant figures over here, I have 2 significant figures here,

They just help me read the number.

Then, in this situation this obviously over here has 4 significant figures, this over here has 3 significant figures.

I wrote it this way because the 5 in 531 is the same thing as 500

And the way to think about this

I count all of the digits, all of the leading 0's behind the decimal, including the leading non zero numeral.

Let me try to take this one step further.

And instead of squaring it this time,

Digits

So I can only have 3 significant figures in my product.

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.

We carry the one, but we carry it into the hundreds place.

This decimal tells you that all three of these are significant.

I'll just call them out as they're called out to me.

321 is 103,041.

So you should have as an answer either a six digit or probably a seven digit number.

Digits

Number of digits

4 Digits

But the whole reason why you're putting a 0 here is because you're now dealing with a 4 in the tens place.

I have to round this to 3 significant figures.

4 and 9 and 8

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

I make sure that it has no more significant figures then either of the numbers that I multiplied.

Well, you count all the digits up to the 2, behind the decimal.

Consider this spiffy, new finite state machine.

Minimum number of digits

Number of Digits