(a) The diameter of Earth at the equator is 12756.27 km. Round this number to three significant

(a) The diameter of Earth at the equator is 12756.27 km....

(a) The diameter of Earth at the equator is $12756.27 \mathrm{~km}$. Round this number to three significant figures and express it in standard exponential notation. (b) The circumference of Earth through the poles is $40,008 \mathrm{~km}$. Round this number to four significant figures and express it in standard exponential notation.

Key Concepts

Rounding Numbers

Rounding is the process of adjusting a numerical value to reduce the number of digits while trying to keep its value close to the original. In many practical applications, especially when dealing with measurements, numbers are rounded to a certain number of significant figures to reflect the precision of the measurement tools or methods used.

Standard Exponential Notation

Standard exponential notation, often known as scientific notation, is a way of writing numbers as a product of a number between 1 and 10 and a power of ten. This format is particularly useful for expressing very large or very small numbers concisely and clearly, while also reflecting the appropriate size and scale of the number.

Significant Figures

Significant figures refer to the digits in a number that carry meaningful information about its precision. This concept is crucial for correctly representing measured or calculated quantities since it informs how much uncertainty is present in the value. When rounding a number, only a specified number of these digits are retained, ensuring that the final result doesn't imply more precision than is actually present.

Transcript

00:01 I want to practice rounding off certain numbers into the desired amount of significant figures.

00:07 So here we have two example numbers.

00:09 We have the diameter of earth's equator, which is this number right here.

00:14 And the second number, which is the circumference of earth at the poles, 40 ,0008 kilometers.

00:20 And so here we want to convert the first number, or we want to express only three significant figures for the first number, and we only want to express four for the second one.

00:30 And so what we want to do is we have to go ahead and round for each of these.

00:34 So for the first one, if we want three significant figures, we're going to have to round up here at the seven, basically.

00:41 And the number that is right next to the seven is a five, and the right next to it's a six.

00:48 So what we can do is go ahead and round up our seven, two, and eight, and make everything else a zero.

00:54 So what we can do when we do that, what it's going to look like, it's going to be 1 -2 -8 -0.

01:03 And that's going to be more or less what we're going to have once we round.

01:08 And if we want to go ahead and express it into a standard exponential notation, remember, we still need to keep the number of significant figures.

01:18 So we still need to keep it as three.

01:19 So we want to express it in exponential notation.

01:22 Well, all we have to do is put 1 .28...

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