Question

How do you write the product of `6.3 times 10^5` and `3.4 times 10^8` in scientific notation?

Answer 1

See a solution process below:

Explanation:

FIrst, we can rewrite the original expression as:

`(6.3 xx 10^5) xx (3.4 xx 10^8) => (6.3 xx 3.4) xx (10^5 xx 10^8) =>`

`21.42 xx (10^5 xx 10^8)`

We can 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))`

`21.42 xx (10^color(red)(5) xx 10^color(blue)(8)) => 21.42 xx 10^(color(red)(5)+color(blue)(8)) => 21.42 xx 10^13`

Now, we can move the decimal point 1 position to the left to put this expression in scientific notation and adjust the exponent for the 10s term by 1:

`21.42 xx 10^13 => 2.142 xx 10^14`