Question

How do you simplify `(8 times 10^8)(9 times 10^10)` and write the answer in scientific notation?

Answer 1

`7.2 * 10 ^19`

Explanation:

A number in scientific notation form is basically two numbers being multiplied.

Remember that multiplication is both associative and commutative.

If we multiply two numbers in scientific notation, we can regroup the numbers as we please.

`(8 * 10^8)(9 * 10^10)`

`=> (8 * 9)(10^8 * 10^10)`

`=> 72 * 10^18`

Now, a number in scientific notation should be in the form

`a * 10^b` where `1 <= a < 10`

Since 72 is more than 10, we need to adjust to satisfy the above condition. We can do this simply by moving the decimal point as many places as we need until the condition is satisfied. However, we need to adjust `b` correspondingly. For every movement of the decimal place to the left, we increment `b` by 1. On the other hand, if the movement is to the right, we decrease `b` by 1

`72.0 * 10^18 = 7.2 * 10 ^19`