[betggray]

Can you do this problem in scientific notation and explain the steps?
5869.3

[jcaron2]

For scientific notation, the goal is to find an alternate way of writing the number so that there's only one non-zero digit left of the decimal point. But we can't just arbitrarily shift the decimal point one way or the other willy-nilly. That would change the value of the number. Our goal isn't to change the value of the number, but rather to find an alternate way of expressing the correct value. Every time you move the decimal point one place to the left, that decreases the value of the number by a factor of 10. (For example, if you take the number 23.5 and you shift the decimal point one place to the left, that gives you 2.35, which is only 1/10 as big as the original number). Likewise, every time you move the decimal point one place to the right, the increases the value by a factor of 10. So to offset this change in value by moving the decimal point we must "undo" it by multiplying by the appropriate opposite power of ten. In my example of 23.5, we can shift the decimal point to the left (which we already saw reduced the value by a factor of 10), so we have to offset that by multiplying the result by 10. Thus 23.5 = 2.35 x 10. Seems kind of trivial, doesn't it? It get's more useful for bigger numbers. For your number, 5869.3, for example, we ultimately want to shift the decimal point 3 places to the left.



Another way of writing this is



That last one is scientific notation: There's only one non-zero digit to the left of the decimal point, and we've written the power-of-10 multiplier using exponents.

Once you've seen how it works, you can simply apply the shortcut that the exponent on the 10 is equal to the number of places you shifted the decimal point left. If you had to shift it right, that would make it a negative number. For example:



The exponent is -4 because you had to move the decimal point 4 places to the right to achieve one non-zero digit to its left.

For the numbers we've used for examples, it still seems kind of useless to go through the trouble of using scientific notation, but it becomes MUCH more useful when you try to solve problems which involve very large or very small numbers. Planck's constant, for example, is 0.0000000000000000000000000000000006626. That would be incredibly tedious to use when solving a problem. It's much easier to write as

Does that make sense?

[Pratik_Pradhan]

In order to scientifically notify a number, You need to know about the exponents. Usually, we use the base as 10. So in order to scientifically notify your number I am performing the following steps:
5869.3=5869.3*10^0
=586.93*10^1
=58.693*10^2
=5.8693*10^3
Thus, 5869.3=5.8693*10^3
If you can understand the last step directly, You need not to see the other steps.
Now, how about notifying scientifically this number:0.0000567?