(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.

Short Answer

Expert verified
(a) The diameter of Earth at the equator, rounded to three significant figures and expressed in standard exponential notation, is \(1.27\times 10^4~\mathrm{km}\). (b) The circumference of Earth through the poles, rounded to four significant figures and expressed in standard exponential notation, is \(4.001\times 10^4~\mathrm{km}\).

Step by step solution

01

Round the diameter of Earth at the equator to three significant figures.

To round the given number \(12756.27\mathrm{~km}\) to three significant figures, we should identify the third significant digit, which is 7. Since the next digit is greater than 5, we need to round up the third significant digit. The rounded number is \(12700\mathrm{~km}\).
02

Express the rounded number in standard exponential notation.

The standard exponential notation of a number is in the form \(A\times 10^B\), where \(A\) has only one non-zero digit to the left of the decimal point and \(B\) is an integer. To convert \(12700\mathrm{~km}\) to this notation, we can rewrite it as \(1.27\times 10^4~\mathrm{km}\). Solution for (b):
03

Round the circumference of Earth through the poles to four significant figures.

To round the given number \(40008\mathrm{~km}\) to four significant figures, we should identify the fourth significant digit, which is 0. Since the next digit is less than 5, we can keep the fourth significant digit as it is. The rounded number is \(40010\mathrm{~km}\).
04

Express the rounded number in standard exponential notation.

To convert \(40010\mathrm{~km}\) to the standard exponential notation, we can rewrite it as \(4.001\times 10^4~\mathrm{km}\). Thus, (a) The diameter of Earth at the equator, rounded to three significant figures and expressed in standard exponential notation, is \(1.27\times 10^4~\mathrm{km}\). (b) The circumference of Earth through the poles, rounded to four significant figures and expressed in standard exponential notation, is \(4.001\times 10^4~\mathrm{km}\).

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