Question

How do you evaluate this `(5.5\times 10^ { 9} ) ( 6.5\times 10^ { - 6} )` and write the result in scientific notation?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(5.5 xx 6.5)(10^9 xx 10^-6) => 35.75(10^9 xx 10^-6)`

Next, use this rule of exponents to multiply the 10s terms:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`35.75(10^color(red)(9) xx 10^color(blue)(-6)) =>`

`35.75 xx 10^(color(red)(9)+color(blue)(-6)) =>`

`35.75 xx 10^(color(red)(9)-color(blue)(6)) =>`

`35.75 xx 10^3`

Now, to write this expression in scientific notation we need to move the decimal point 1 place to the left so we need to add to the exponent of the 10s term:

`35.75 xx 10^3 => 3.575 xx 10^4`