How do I convert 0.000000000000000000000327 into scientific notation?

Question

How do I explain it into words?

Answer 1

Dear Charley,

 

We already know that 0.000000000000000000000327 in scientific notation is going to be

 

3.27 * 10^-n where n is what we are trying find.

 

Count the number of zeros between the decimal point and the 3, then add one to it.  This gives 22

 

3.27 * 10^-22

 

 

Answer 2

When you write a number in scientific notation, you write it as a product of two numbers: the first number is a number between 1 and 10 (greater than 1 but less than 10) and the second number is a power of 10.

You use scientific notation to eliminate trailing zeroes and zeroes that precede non-zero digits. You cannot eliminate zeroes that are between non-zero digits, however.

 

In your problem all the zeroes preceding 327 can be eliminated. You have to keep all non-zero digits and all zeroes that fall between non-zero digits. You keep the 327 in that order !

Where do you put the decimal point so that the number is between 1 and 10 ?

0.327 ?, 3.27 ?, 32.7 ?, 327. ?

0.327 is less than 1 and 32.7 and 327. are greater than 10 so the answer is 3.27 !

3.27 is our first number. The second number must be a power of 10.

Look at the decimal point in the number 3.27; how many places and in which direction must it be moved to get back to the original number ? You must move the decimal point 22 places to the left to get back to the original number. Remember, you cannot change the value of the original number, only the way it is written.

The final answer is 3.27*10^(-22). You have to move to the left past the 3 and put 21 0's in front of the

327 ! Why is the exponent negative ? The exponent is negative because you moved the decimal point to the left. If you move the decimal point to the right, the exponent will be positive.

Example: 4,309,000,000=4.309*10^9

Finally, if either number is 1, you can leave it out of the answer.

Example:10,000=1*10^4=10^4

Example:8.36=8.36*10^0(anything to the zero power is 1 except 0 to the zero power which does not exist)

8.36=8.36*10^0=8.36*1=8.36(in other words, don't change 8.36 because it is already between 1 and 10)

Answer 3

3.27x10^-22

 

Informal answer:

 

3.27 is a good choice for the front of the number because it's a number between 1 and 10.  Basically, you just count how many digits the decimal point had to jump to get there.  The little "." skipped over 21 zeros and then over the digit "3" to land right between the "3" and the "2"--that makes a change of 22 places.  It had to move to the right, so we make that 22 negative and put it as the power of 10.

 

Another way to look at it is that 0.000000000000000000000327 is very small.  Literally it's the same thing as

0.0000000000000000000001 X 3.27

 

Then we just recognize that 0.0000000000000000000001 is the same thing as 10^-22 (using the same counting zeros method)--so instead of that long number, we can now write it

 

10^-22x3.27       -or the normal way-      3.27x10^-22

 

I guarantee that even fancy scientists sit there with their index fingers counting how many zeros that the decimal point has to jump just so they can put that number over the 10.

 

Technical answer:

 

You express a particularly large or small number in terms of an expression with a power of 10 to save space and preserve precision.  You divide the number by a power of ten such that the number becomes greater than or equal to 1 and less than 10.  Then you just write the answer next to the power by which you divided it.

Answer 4

You move the decimal point until there is one and only one digit

to the left of the decimal point -in the ones place -

and so all other digits are to the right of the decimal.

 

>>  3.27

 

Now you count how many places you moved the decimal point.

And this number 'n' becomes the exponent of the power of 10.

 

>>  3.27 x 10ⁿ

 

In this case you moved it 22 places to the right.

0_^000 000 000 000 000 000 000 3_^27

 

>> 3.27 x 10^±22

 

Now you have to decide on the sign of the power of 10.

If you moved the decimal to the right the sign is negative (-).

If you moved the decimal to the left the sign is positive (+).

 

In this case you moved the decimal to the right so the sign is negative.

 

>> 3.27 x 10^-22

 

Answer 5

With 10^0 = 1 as a start, the general rule is that for every position to the right of the decimal point the first (most significant) digit is, subtract one from the exponent. Thus, 0.1 = 10^(0-1) = 1 * 10^(-1), .01 places the 1 two positions right of the decimal point, so .01 = 1.0 * 10^(-2), and so on. Remember, it's based ONLY on the most significant digit, so a number like .0005609 = 5.609 * 10^(-4).

 

What such notation actually means is this: 10^(-i), where i is any real number, is the representation of 1/[10^(i)]. So 10^(-1) is 1/10^1 = 1/10 = 0.1. Thus, 10^(-2) = 1/[10^2] = 1/100 = .01, and so on.

 

In you case, the 3 is in the 22nd position right of the decimal point, so in scientific notation, your number would be 3.27*10^(-22).

 

You may sometimes see this written as 3.27E-22. That's how computers used to portray numbers in scientific notation. In this case, 'E' is not the 'e' (=2.71...) of logarithmic notation; it stands for 10^.

 

Hope this helps.