Saturday, January 21, 2012

Scientific Notation and Sig Fig help?

How would you put them in scientific notation?



1. 20.0890



2. 199.900



3. 35,000



Round off these numbers until you get to 3 sig figs.



1. 20.0890



2. 199.900



3. 35,000



Thank You! I have my first Chem. test tommarow!

Scientific Notation and Sig Fig help?
Scientific Notation:

1. 20.0890

If you want to turn this into scientific notation, you see where the decimal place is? Move that little dot to the left or right so that you only have 1 digit on the left. So, since it is 20.0890, you can move the DOT one place to the left and you have 2.00890

Now since you moved it over 1 place, it is 2.0089 * 10^1

If you want to test it, you can do the math and you will see that if you times 2.0089 by 10^1, you will get the original answer.



2. 199.900

With this one, you are going to have to move that little decimal POINT to the LEFT two place to get the first digit by itself. You would now have 1.99900

BUT, you have to times that by some POWER of 10. Since you moved it over 2 places, it would be 1.999 * 10^2

You see how I raise the ten to the number of times I moved the decimal point over?



3. 35,000

For this one, you have to add your own decimal point since it is not given to you.

You probably know that 35,000 is the SAME as 35,000.0 (that POINT 0 doesn't affect the number at all, right?) To get the first digit by itself, move that decimal point to the LEFT 4 times. You would now have 3.5, but then you have to times that by 10^4 (you moved it over 4 times)



Sig Figs:

1. 20.0890

Rounding Sig Figs is basically the same as rounding any number. Since you have to round it to THREE sig figs, you can start with the first REAL number (don't count zeros!), in this case it is 2. Then, go over 3 figures and you are at the second 0. Now, you know that that 2nd 0 is the one you are going to have to round. Since the number to the RIGHT of that 0 is GREATER than 5, you round up!

The answer would be 2.01.



Do you get it?



2. 199.900

With this one, start with the 1 as your first sig fig. Then move over 2 (so you moved over 3 total) and you are at the 2nd 9. Since the number to the RIGHT of that 9 is GREATER than 5, you would round it up. Since 9 can't round up to another number, you have to also round the number to the left of it. Since that number is a 9 as well, you have to round up the number to the left of THAT, until you get to a lower number.

The answer would be 200 because of the rounding.



3. 35,000

For this one, the answer isn't any different. There are only TWO sig figs in this number to begin with. Any place holders (like 000,000,000) don't count as sig figs. Since this only has 2 figures, it just stays the same



:)







To round this "0.00250" to 3 significant figures, you would go to the first REAL number, like before. Since 0s don't count as real numbers WHEN THEY ARE AT THE START, you would start with 2 as the first sig fig. Move over 3 and you are at the 0. Since there are no numbers to the LEFT of 0, you don't have anything to round and your answer stays the same

The answer is .00250 :)
Reply:1. 2.0089 X 10 to the first power

2. 1.999 x 10 to the second power

3 3.5 x 10 to the fourth power



rounding:

1 20.089

2. 199.900

3 35,000


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