Question

0.39 x 10^9

Put in scientific notation ​and explain how it works.

Answer 1

3.9 x
`10^(8)`

Explanation:

0.39 is not in scientific notation. For a number to be in scientific notation the first factor has to be 1 or greater, but less then 10. 0.39 is less than one.

First we must write 0.39 in scientific notation. We need to move the decimal so that the number is greater than 1, but less than ten. If we move the decimal one place to the right, we get 3.9. The standard number is smaller than 3.9. How much smaller?
`10^(-1)` smaller.

0.39 in scientific notation would be 3.9 x
`10^(-1)`. We cannot forget the
`10^(9)`, so our number looks like this now:

3.9 x
`10^(-1)` x
`10^(9)` The product of powers principle tells us that if we have powers with the same bases, we can add the exponents.

3.9 x
`10^(-1+9)`

or 3.9 x
`10^(8)`