Question

the order of magnitude of 2^20 will be? (in terms of physics).

Answer 1

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

here we have to find out order of magnitude of 2^20.

first resolve 2^20 into m × 10ⁿ

so, 2^20 = (2^4)^5 = (16)^5

= (1.6 × 10)^5

= (1.6)^5 × 10^5

= 10.48576 × 10^5

= 1.048576 × 10^6

≈ 1.05 × 10^6

here it is clear that, √10/10 < 1.05 < √10

so, 6 is order of magnitude of 2^20.

Answer 2

Answer: The order of magnitude of 2^20 is 6

Explanation:

We know that order of magnitude can be found out only when we have a function like a x 10^b. In this case the power of 10 is considered as the order of magnitude

But here we are given with 2^20

So we solve this question like this

2^20 = 2^10 X 2^10

We just need to find the value of 2^10 or it can be further simplified as

2^10 = 4^5 and so on

But here I am going to show the direct method

So,

2^10 = 1024 ( calculation done in the attachment )

Therefore,

2^20 = 1024 X 1024

1024 is nearly equal to thousand or the other thing which can be said is that

1024= 1.024 X 10^3

Here the order of magnitude is 3 and 0.024 are not significant

Thus,

2^20 = 10^3 X 10^3 = 10^6

Thus the order of magnitude is 6

THESE CALCULATIONS ARE DONE WITH RESPECT TO OBJECTIVE QUESTION HENCE ALL THE ASSUMPTIONS ARE JUSTIFIED

HOPE YOU ARE SATISFIED