Questions about scientific notation and significant figures?

Question

If you assume there are three significant figures in the number, would 72,000 = 7.20 x 10^2 or 7.20 x 10^4? The significant numbers should be the "7,20" right?

If you write the following in standard, nonexponential form would 3.86 x 10^-6 = 0.00000386?

If you write that same number in common decimal form, is it the same? If so, why would it be specified to write them in "common decimal" instead of "standard, nonexponential" form?

Man, I thought I understood this stuff when I left class, haha...

Okay, I see where I got confused on the first one, I was thinking three significant figures in 72,000 as 720 (which doesn't even make sense); instead of three significant figures in my answer 7.20. I read it wrong, haha. Thanks :)

Answer 1

72,000 = 7.20x10^4. It's just a matter taking the three significant figures, and then multiplying by the correct place holder. 72000 has five digits bore the decimal, so we multiply by 10^4

As for the difference between common decimal, and standard nonexponetial, I think they are the same form and 3.86 x 10^-6 is indeed 0.00000386 in common decimal form.

Answer 2

Just remember that it's only significant if they give you the digit.

ie: 7.20 * 10^4 (or 72,000). You only have 3 significant figures: the ten-thousands, the thousands, and hundreds. But if they gave you 72,000, you actually have 5 sig figs...

If you're at the other side of the decimal point, it's still the last place they give you.

ie: 3.14881 * 10^-7. You don't stop at the 7th place (whatever it's called), you keep going until you hit that 1 they gave you!

iie: 2.50 * 10^-2. That 0 is significant enough that they wasted ink telling you. take it all the way to the ten-thousandths place.

Answer 3

It's 7.20 x 10^4. However many places you're moving the decimal point is the exponent of the power of ten.

In 3.86 x 10^(-6), move the decimal point six places to the left (and fill in the placeholders with zeroes, of course).
It's 0.00000386

My guess is the reason they refer to decimal numbers without scientific notation as "common decimals" is because different terminology is used in different countries. In the UK, what we call "scientific notation," they call "standard notation." If a US text says to write something in standard form or using standard notation, a student from the UK would write it in scientific notation.

Answer 4

72,000 = 7.2 x 10^4, with only two significant figures
"3.86 x 10^-6 = 0.00000386" is correct

Answer 5

I think you've got it! 7.20 *10^4 for the first one.