I am no Euclid or Ramanujan but the mathematician in me was flabbergasted. *What on earth did I just hear*?!

Me: Noo, that can’t be. They are the same value, 1!

B: First of all, tell me what is the importance of scientific notation?

Me: (some shitty answer about increased readability, easier comparison blah blah)

B: Ok so there is always some amount of uncertainty in every measurement. Suppose you calculate the dimensions of an object using a vernier caliper and arrive at the value 1.41cm.

You’re completely sure of 1.4 but the 1 following 1.4 is uncertain.

How many significant digits does this value have?

Me: Three of course! (come on, that was easy peasy)

B: So in the next step you measure using screw gauge for extra precision.

The new measurement is say, 1.414cm.

Now you can be dead sure that 1.41 is correct and the 4 following the 1.41 is still uncertain.

How many significant digits are there now?

Me: Four.

B: Right, in scientific notation it would be 1.41 x 10^{0}cm and 1.414 x 10^{0}cm.

If you were to calculate the dimensions of the same object in another world where the unit of measurement is kilometer,

1.41cm would be-?

Me : 0.00141km.

B: What would happen to the number of significant digits?

Me: It becomes six? (gaping and still not able to figure out what this has got to do with 1, 1.0 and 1.00)

B: The number of significant digits in any world should not change.

That is why we use scientific notation. So 1.41cm will be 1.41 x 10^{-5}km, and thus the number of significant digits is the same in both cases. Three.

So now you know why 1, 1.0 and 1.00 are different.

Me: (bulb inside my head finally lit up) They have 1, 2 and 3 significant digits respectively!

Conversations with the Brother always leave me feeling intellectually impaired.

I feel my whole life was a lie now 😦 (physics in this way?! )

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HAHAHA! Welcome to my world 🙂

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