express 0.0103240 in scientific notation.?

Question

i have 2 options for an answer which its
1.03240 * 10 square root negative 2 which it equals to .010324
but then i also have
1.0324 * 10 square root -2 and it equals the same thing.
but i mean whats the right answer if both equal the same and the only thing that changes is that one has a 0 at the end and the other one doesnt?

Answer 1

Square root is inappropriate here. The correct answer is:
1.03240 x 10^-2. Since the last zero was present in the original, it is assumed to be a significant figure.

Answer 2

Am I reading this right? The way I understand scientific notation, 0.0103240 would be expressed as

10324 X 10^-6
(read: 1-0-3-2-4 times 10 to the negative sixth power)

because the zeroes are placeholders and the decimal in your original number is six places to the left of 4, the last and therefore lowest value whole number.

Technically, there IS no difference between the two expressions you're given as an answer because the zero has no value, but I'm reasonably sure the answer you're looking for will be the first due to the final zero in the original problem.

Answer 3

1/ zeroes at the right of a number that contains a decimal point have no meaning 1.2 = 1.20 = 1.200 = 1.2000000000000000
so you can ignore them always

2/ negative 2 and -2 are the same so in fact you ask twice the same computation and quite logically you get twice the same answer (written in a sligthly different way)

3/WARNING: you seem to confuse 10 raised to power -2 which is equal to 0.01 and 10*square root(-2) which is the imaginary number j*1.4142...

I guess from your explanation you incorrectly wrote 10 square root -2 while you meant 10 raised to power -2

Answer 4

1.0324 * 10^-2. You only keep the significant digits in the mantissa, so you drop the zero. By the way, in scientific notation, there's the mantissa (the number) and the exponent (the power is it raised to) so you don't say "10 square root negative 2" you say 10 raised to the -2 power

Answer 5

The second one is the most correct since the extra 0 is implied and does not need to be written.

Answer 6

1.03240 x 10 ^-3
is that right? o_O the way you have it was confusing since i never learned it that way. sorry if this is the wrong explanantion. X]
but i don't really think the last zero makes a difference because it only adds one more decimal place [i think this would matter if this involved sig figs... i think].