Decimal Places and Scientific Notation?

Question

0.0005 to 2 decimal places is 0.00

But can 5 x 10^(-4) be written as 0.005 x 10^(-2)?? Or it's not accepted because it's not in scientific notation? So it has to be written as 5.00x10^(-4)? And what's so special about scientific notation?

Answer 1

scientific notation is a way to easily see how large something is. .0005 is easier than 5*10^ -4, but 5*10^37 is much easier than 50000000000000000000000000000000000000.

as for your beginning problem, is that suppose to be decimal places or significant figures. because as sig figs, it would be written as .00050, since zeros in between the decimal and a number do not count as sig figs.

Answer 2

What's so special about scientific notation is that it allows you to deal with extremely large and small numbers.

with 1,200,000,000,000,000,000,000,000,000,00... you would have to count the zeros. 1.2 x10^36 takes less space and is less likely to cause errors.

if you multiply 1.2 x 10^36  by 5 x 10^-40 you get 1.2 x 5 = 6 to the 10^36 * 10^-40 = 10^(36-40) = 10^-4

so 6 x 10-4 , which is easier than dealing with all the zeros.

Answer 3

should be 5.00*10^-4. It is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation.