Question

How do you write 12,040,000,000,000 in scientific notation?

Answer 1

`1color(red)(2,040,000,000,000.) = color(blue)(1.204) xx 10^color(red)(13)`

Explanation:

Scientific notation is written as a product of `color(blue)("a number") and color(red)("a power of"10`

The number must be a number written as `color(blue)(1<= n <10)`
This means there must only be `1` digit before the decimal point.

Move the decimal point from the end of the number to between the `1` and the `2`
Count how many place holders there are to achieve this, and that becomes the power of `10.`

`1color(red)(2,040,000,000,000.) = color(blue)(1.204) xx 10^color(red)(13)`

Answer 2

`1.204xx10^13`

Explanation:

The first step to putting it in scientific notation is to put the new decimal point in such a way that the number is between 1 and 10. In this case, that means putting the decimal point between the 1 & 2, to give 1.2040000000000 = 1.204 (because the zeros don't mean anything after a decimal point if there's no other digit after them.

Now we have to count the number of places in between the new decimal point and the original decimal point. The digits 2040000000000 are between the new and old decimal point, so that gives us 13.

12,040,000,000,000 is bigger than one so our exponent is +13 (whereas if it was 0.0000000000001204 it would be -13), and thus our number in scientific notation, also called standard form, is:

`1.204xx10^13`