Question

The masses of four planets in a solar system outside the Milky Way are given below.

Planet A: 5.97*10^24
Planet B: 3.30*10^23
Planet C: 1.89*10^27
Planet D: 4.87*10^24
What is the order of these planets from least to greatest?

Answer 1

The answer is B, D, A, C.

Let's all of them have the same exponent so we can compare them. Let 23 be the common exponent since it is the smallest one:
Planet A: 5.97 * 10²⁴ = 5.97 * 10¹⁺²³ = 5.97 * 10 * 10²³ = 59.7 * 10²³
Planet B: 3.30 * 10²³
Planet C: 1.89 * 10²⁷ = 1.89 * 10⁴⁺²³ = 1.89 * 10⁴ * 10²³ = 1.89 * 10,000 * 10²³ = 18,900 * 10²³
Planet D: 4.87*10²⁴ = 4.87 * 10¹⁺²³ = 4.87 * 10 * 10²³ = 48.7 * 10²³

Since 3.30 * 10²³ < 48.7 * 10²³ < 59.7 * 10²³ < 18,900 * 10²³, then the order of these planets from least to greatest is B < D < A < C