Scientific notation and significant figures

Last week my Chemistry class reviewed scientific notation (S.C.) and significant figures (S.F.). I used to think that you could only use scientific notation with whole numbers, but I now know that you can use this notation with decimals as well! Scientific notation makes writing really big or small numbers easy.

Scientific notation

Let's start with whole numbers. An example of a whole number in S.C. looks like this:85000000 = 8.5 x 10^7.

The first thing you need to do is count from the right side until you get to the first number (it takes 7 times to get to the first number, 8)

Next, you put a decimal after the first number and then leave all number behind (unless it's a zero), so it looks like this: 8.5

Then, you add ' x 10' after 8.5, so it looks like this: 8.5 x 10.

Now, remember when you had to count how many times it took to get to the 8? Well, that number (7) is the final part to scientific notation! You simply add ^7 right after the 8.5 x 10, so the finish product looks like this : 8.5 x 10^7.

For finding scientific notation for decimals, you do the same process for finding whole number S.C. The only two differences are that you start from the left side and that the exponent is negative. For example: 0.000253 = 2.35 x 10 ^-4. So, you start on the left side and it take 4 times until the decimal is after the 2. You have a negative exponent because you are coming from the left.

Significant figures

Now, finding significant figures means the numbers that matter in a calculation. To find S.F. is simple, just use the America, Pacific and Atlantic ocean!

The Pacific Ocean is used for decimals, (the P stands for period) and the Atlantic Ocean is used for whole numbers (the A stands for absent a period). The first thing you have to do is figure out if the number is a decimal or whole number.

The example I'll use is 22. This number will be on the Atlantic side, which means you'll have to start on the right side of the number and count the numbers (not including zeros). So, 22 has 2 S.F.

If there is a number like 4572630001, you still start on the right side and since the number 1 is the first number and the zeros come after 1, you will count the zeros as well. So, this number has a total of 10 S.F.


The example I'll use for the Pacific side will be1.085. This number has a total for 4 S.F. To figure out how many S.F. a decimal has, you start on the left side of the number and count. For 1.085, there are 4 numbers, so the S.F. is 4

If there is a number like 0.009, you still start on the left side, but don't count until you get to a number other then 0. This leaves us will 9, meaning that 0.009 only has 1 S.F.