The reason why you write it like that is the first number is never behind the decimal always before, then all the numbers after that until it hits zero is written after the decimal (unless its a number like 1203300 then you write 1.2033). Then you count how many numbers there are, except the first one and that will be your exponent. It will always be x 10^exponent.

When you have 0.010 you just write it as 1x 10^-2. You get negative 2 because your going backwards. You put the decimal after the one and then count how many times it takes til the decimal was where it was orignally.

Well thats how I understand it. I hope I didn’t confuse you! Good luck with your math!

Have you ever done a calculation and had 20 digits after the decimal? Well, most of the time, all those digits don’t mean anything, because the original numbers used in doing the calculation were not known that accurately.

In scientific notation, EVERY digit reported is significant and the scientist knows that.

For example, if you saw the number 2700, is that approximately 2700? Or is it EXACTLY 2700? If you wrote it 2.7 x 10^3, it would tell the scientist that you meant it to be approximate, because only the 2 and 7 are significant. If you wrote it 2.700 x 10^3, the scientist would know that you meant all 4 digits to be significant, because those are the rules of writing numbers in scientific notation. And if you wrote 2.70 x 10^3, then only 3 digits would be significant. This gives the scientist important information.

Now for the rules of conversion:

To convert a number INTO scientific notation, you might follow these 6 simple steps.

1. Find the significant digits.

2. Write the first digit. Then follow it with a decimal and all the rest of the significant digits.

3. Next, just concentrate on the first digit and ignore the rest of the number.

4. Then ask this question: The first digit times (or divided by) what number will give me back the number I started with?

5. Convert the answer to Step #4 to a power of 10.

6. Write the completed scientific notation.

So, 87,560 would be 8.756 OR 8.7560 depending on whether or not the zero was just a placeholder or if it was actually a measured zero. Then ignore all the digits except the 8 and ask, what do I have to multiply 8 by to get back 80,000? The answer is 10,000, so this is 10^4. Therefore, the answer is either 8.756 x 10^4 or 8.7560 x 10^4.

With numbers smaller than 1, as in 0.010, the same rules apply. Write the 1. Then write the decimal and any significant digits behind it. (As it turns out, final zeros found AFTER the decimal are significant.) So the only correct conversion of this number would be 1.0. Then ask, “What would I multiply (or divide) 1 by to get 0.01? The answer is we have to DIVIDE by 100 or 10^2, because 0.01 is smaller than 1. Now, when you divide by a power of 10, the exponent is negative. (This is convenient, because the negative sign looks like a little division bar and it will help you remember.) So your answer would be 1.0 x 10^-2.

Please let me know if this helps.

87,560 = 8.7560 x 10,000 = 8.7560 x 10^4

= 8.7560E+4

Similarly,

0.010 = 1.0 x 1/100 = 1.0 X 10^-2

= 1.0E-2

It is rare that 4 decimal places are significant, but again this can only be determined by context.