How would you write the number 3.000052 in scientific notation?

The purpose of scientific notation is to write a non-zero number with a lot of digits to a shortened version of the number with less digits. Scientific notation is expressed as a x 10^n where a is more than 1 and less than 10 and n is any integer (positive and negative whole numbers and 0).

For the number 3.000052, it's already more than 1 and less than 10 so we can set a as 3.000052 but we still have to figure out what n is. If n=1 then we would have 3.000052 x 10^1 which is the same as 3.000052 x 10 which is 30.00052, which isn't what we want. Instead we make n=0 which makes 10^0=1 because any number raised to the 0 power is 1. Therefore we have,

3.000052 x 10^0 = 3.000052 x 1 = 3.000052.

So your final answer is 3.000052 x 10^0.


In scientific notation, a real number x is written as a * 10^n. Here n must be an integer (positive, negative or zero) and a must be a real number (positive or negative) with the absolute value between 1 and 10 (excluding 10).
Only nonzero numbers can be written in scientific notation.
Now, let's look at the given number. If it is x =3.000052, then it is already in the scientific notation, with n = 0 and a =3.000052.
Because of this, I suppose that leading "3." is the number of your question, and the number is actually .000052, or 0.000052. In this case, we need to multiply it by 100000 = 10^5 to come up with a value of abetween 1 and 10: 5.2. To come up with our value for n, we switch the sign of the exponent on 10 that we have just used; since we multiplied our original number by 10^5, n is -5, and the scientific notation of 0.000052 is 5.2 * 10^(-5).
https://www.mathsisfun.com/numbers/scientific-notation.html

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