when do u move the decimal in scientific notation?

Question

and where?

Answer 1

Well, you move the decimal to make something into scientific notation. And usually, you move it so that it's after the first number from the left.

For example, let's say you have the number 120.

In scientific notation, it'd be written as 1.20 x 10^2.

The reason you write it that way is because you're moving the decimal place to the left two places. And when you move the decimal place, you're multiplying by a power of 10. 10^2 = 100 = two decimal places.

Another example is 1340.

1340 would be written in scientific notation as 1.34 x 10^3. You moved the decimal place over three places. So that's 10^3 power.

Does that make sense?

Answer 2

Brian L's answer was really good, I'd like to expand on it a bit.

His example of 1340 being 1.34 * 10^3 is right and this is the most proper way to express it in scietific notation. It has only one number to the left of the decimal point and put all other numbers to the right. Count how many places that you had to move the decimal point to make your number have only one number on the left of the decimal point. This is what you will use as the exponent of the 10. If your decimal point moves to the left, the your exponent is positive, if it moves to the right then the exponent is negitive.

So in his example, he moves the point 3 places to the left, only because he wants his number in this form, which is best:

1340 becomes 1.340

now the eponent of the 10 will be 3 because you moved it 3 places to the left.

1.340 * 10^3

But this is not the only form you can put the same number in. You could also write it as:

134.0 * 10^1
13.40 * 10^2
1.340 * 10^3
0.1340 *10^4
0,01340 *10^5

or

13,400 * 10^-1
134,000 * 10^-2
etc...

The form Brian shows is the most proper, but sometimes you don't neccessarily want to have one digit to the left of the decimal point. For example, when working with metric, it's usually better to have your expontents be some multiple of 3 or -3 so they match up better with the whole Milli, Kilo, Mega thing.

I hope this helps you

Answer 3

Best way to think of it is, in scientific notation your numbers have to be between 1 and 9 to make life easy.
so move your decimal to the right of your left most (1-9) digit and adjust the power of 10 accordingly like this:

0.003487 becomes 3.487 x 10^-3
759.47 becomes 7.5947 x 10^2
46.2x10^2 becomes 4.62 x 10^3
and
3.98 remains 3.98 or 3.98 x 10^0

Remember if you move the to the left then the power of 10 gets a positive number equal to the number of places you moved the decimal added to the existing power of 10 and a move to the right is a negative power of 10 by as many places as the decimal point moved added to the initial power of 10. In most cases the initial power of 10 is 0.

Answer 4

to the nearest whole number or place value