Question

Estimate the order of magnitude of the radius of the earth. Take the radius of the earth = 6400 Km

Answer 1

Estimate the order of magnitude of the radius of the earth. Take the radius of the earth = 6400 Km...

answer : order of magnitude of the radius of the earth is 10^7.

explanation : order of magnitude : it is used as scientific notation. if any number X in such a way that X = m × 10^n , where m belongs to $\left[\frac{\sqrt{10}}{10},\sqrt{10}\right]$ then, 10ⁿ is known as order of magnitude of that number.

here given, earth's radius 6400 km

it can be written as 6400000m [ as we know, 1 km = 1000m]

so, 6400 km = 6400000 m

now, 6400000m = 0.64 × 10^7 m

here you can see √10/10 ≤ 0.64 < √10

so, 10^7 is the order of magnitude.