If i had to round 84791 to four significant figures would it be 8479?

Question

and another question.

if i had to round 136758 to four significant and turn it into scientific notation how would i do so?

please explain!!

Answer 1

Significant digits are digits that have more meaning that just keeping the decimal place in the right spot.  If the decimal point establishes magnitude (or "bigness") then the significant digits establish precision (or "exactness").

Look at this series:

80,000

85,000

84,800

84,790

84,791

84,791.3

84,791.25

Each of these numbers is in the tens of thousands.  The decimal point stays where it belongs.  The change in how many significant digits there are doesn't change the overall magnitude of the number.  All of these numbers have about the same "bigness" to them.  They just keep getting more and more precise about the exact amount of, well, whatever it is.

Pretend that there are 84,791.25 miles between your home and mine.  There's nothing wrong with saying that there are about 85,000 miles between us.  That's a less precise measurement, but it's still about the same thing.

Rounding to a given significance should always leave you with about the same thing.  84,791 rounds to 84,790.  Actually, so does 84,791.25 miles.

The decimal point is one way to show the "bigness".  Orders of magnitude is another way.  That's what scientific notation is about -- using orders of magnitude instead of a bunch of zeros to keep the "bigness" right.

136,758, rounded to 4 significant digits, is 136,800.  But, we can use powers of ten (which we call orders of magnitude) to represent the bigness, instead of those two zeros at the end of 136,800.

136,800 * 10^0 = 136,800

13,680 * 10^1 = 136,800

1,368 * 10^2 = 136,800

136.8 * 10^3 = 136,800

13.68 *  10^4 = 136,800

1.368 * 10^5 = 136,800

The simplicity here is, you can count how many places you move the decimal, and that's the power (exponent on the 10) you use to multiply the number back up to the correct "bigness".

With scientific notation, no one has to wonder which zeros mean anything.  For instance, if I round 120123 to three significant digits, it looks like 120000.  Which looks like it's just two significant digits.  But, if I round 1.20123 * 10^5 to three significant digits, it looks like 1.20 * 10^5 -- three digits means three significant digits.  No confusion.

There's a reason for keeping this "bigness" in mind.  For instance, if I want to go to your best friend's house, that might mean that I go to your house, then his.  Let's say he lives a quarter mile away from you.  My traveling distance (if I know it so exactly) is 84,791.25 plus 0.25, so 84,791.50.

But, if I only told you that I'm 85 thousand miles from you, and someone asks you how far I'll travel to get to your friend's house, it'd be silly for you to say "about 85 thousand and a quarter miles".

All of this significant digit counting keeps us from making the same kind of silly mistakes when we're doing scientific math.  While we're doing chemistry and physics, we'd like to avoid doing math that means the same as saying "yeah, it's 85 thousand miles, give or take a few hundred miles, plus another quarter mile."

Answer 2

You need to keep the zero where the 1 originally was: 84790

The other would be 1367 but the 5 after the 7 rounds the 7 up to 8 then put zeros as placeholders for the 5 and 8: 136800

then move the decimal point 5 places left so 1.368 X 10^5