Round each of the following numbers to three significant figures and express the result in stand

step 1 Exploring the concept of significant figures. And using a variety of examples here. So significa

Round each of the following numbers to three significant...

Key Concepts

Rounding

Rounding is the process of adjusting a number to a required degree of precision by modifying the least significant digit based on the subsequent digit. This method is particularly important when expressing numbers with a fixed number of significant figures to maintain consistency and accuracy.

Scientific Notation

Scientific notation, also known as standard exponential notation, is used to express very large or very small numbers in a compact form as a product of a coefficient (a number between 1 and 10) and a power of ten. This notation simplifies calculations and comparisons by maintaining a consistent format for representing numbers.

Significant Figures

This concept refers to the digits in a number that carry meaning contributing to its precision. When rounding to a specific number of significant figures, it is important to identify and retain only the first few meaningful digits, ignoring extraneous zeros that do not affect the value’s precision.

Transcript

00:01 Exploring the concept of significant figures.

00:03 And using a variety of examples here.

00:06 So significant figures by definition, there are each of the digits of a number that are used to express it to a certain point of accuracy.

00:14 And so what we want to do with these numbers here is that we want to go ahead and round each of them to three significant figures and then express them in exponential notation.

00:26 And so let's go ahead and start with the first one.

00:29 So if we want to go ahead and express this number as three significant figures, we're going to have to round it.

00:36 And then the point in which we would have to round is over here.

00:41 If we can see that the number right next to four is an eight, so if it's great, eight is greater than five.

00:47 And so we can go ahead and round this number.

00:51 And it will look like this, 205, and then one, two, three, four.

00:58 So this is going to be the number that we get once we round.

01:01 So we see now we have three significant figures.

01:04 These zeros do in fact do not count as significant digits in any case.

01:11 And so if you want to go ahead and write that in standard exponential notation, all we would have to do is simply express this as three significant digits.

01:20 So 2 .05.

01:22 And if we want to go ahead and multiply that by 10 to the 5.

01:27 Want to go ahead and double check everything, you can plug this number into your calculator, and that will get you this number right here, with the zeros included.

01:36 So we're not changing the number whatsoever.

01:39 We're not getting rid of the zeros necessarily.

01:40 We're just expressing it to be three significant figures only.

01:45 The second number here, again, we're still trying to express it as three significant figures.

01:50 And so the point in which we will go ahead and round is here.

01:55 The numbers that's next to two is a nine, which is greater than five.

01:58 So we can round this two up to a three.

02:00 So the way in which now this would look like would be 0 .002 .23, 293, like so.

02:13 So now that we've rounded everything, we can go ahead and try to write this an exponential notation...