Problem 38 - Chemistry: The Central Science

Question

(a) The diameter of Earth at the equator is \(7926.381 \mathrm{mi}\). 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.

Step-by-Step Solution

Answer

(a) The rounded diameter of Earth at the equator is approximately \(7.93 \times 10^3 \mathrm{mi}\). (b) The rounded circumference of Earth through the poles is approximately \(4.0008 \times 10^4 \mathrm{~km}\).

Step 1: Rounding to significant figures#a

a) The diameter of Earth at the equator is given as \(7926.381 \mathrm{mi}\). We'll round this to three significant figures. To round to three significant figures, we look at the fourth digit. Since it is greater than 5, we'll round the third digit up. Therefore, the rounded number is: \(7926.381 \approx 7930\) b) The circumference of Earth through the poles is given as \(40,\!008 \mathrm{~km}\). We'll round this to four significant figures. To round to four significant figures, we look at the fifth digit. Since it is less than 5, we'll leave the fourth digit unchanged. Therefore, the rounded number is: \(40,\!008 \approx 40,\!008\)

Step 2: Expressing in standard exponential notation#a

a) The rounded diameter of Earth at the equator, \(7930 \mathrm{mi}\), can be expressed in standard exponential notation by moving the decimal point 3 places to the left. This gives us: \(7930 = 7.93 \times 10^3 \mathrm{mi}\) b) The rounded circumference of Earth through the poles, \(40,\!008 \mathrm{~km}\), can be expressed in standard exponential notation by moving the decimal point 4 places to the left. This gives us: \(40,\!008 = 4.0008 \times 10^4 \mathrm{~km}\)