Question

How do you simplify `1,000,000,000\times 6,000,000,000`?

Answer 1

See a solution process below:

Explanation:

We can rewrite this as:

`(1 xx 1,000,000,000) xx (6 xx 1,000,000,000) =>`

`(1 xx 6) xx (1,000,000,000 xx 1,000,000,000) =>`

`6 xx (1,000,000,000 xx 1,000,000,000)`

To multiply the numbers on the right we combine the number of `0`s `xx 1` giving:

`6 xx (1,color(red)(000,000,000) xx 1,color(blue)(000,000,000))`

`6 xx (1,color(red)(000,000,000),color(blue)(000,000,000)) =>`

`6,000,000,000,000,000,000`

Answer 2

Alternatively, using scientific notation makes things easier (even though it's technically the same method).

The answer is `" "6 xx 10^18 " " or " " 6,000,000,000,000,000,000`

Explanation:

`1,underbrace(000,000,000)_(color(red)"9 ""zeros") = 1 xx 10^color(red)9`

`6,underbrace(000,000,000)_(color(red)"9 ""zeros") = 6 xx 10^color(red)9`

Therefore:

`1 xx 10^color(red)9 xx 6 xx 10^color(red)9`

`= (1 xx 6) xx (10^color(red)9 xx 10^color(red)9)`

`= 6 xx 10^(color(red)9 + color(red)9)`

`= 6 xx 10^color(blue)18`

`= 6,underbrace(000,000,000,000,000,000)_(color(blue)"18 ""zeros")`

Final Answer

Answer 3

6,000,000,000,000,000,000

Explanation:

`6 * 1=6`

now add the Zeroes after 6
`(00000....)9 zeroes + (00000...) 9 zeroes = 9+9=18`

Write `6` and add `18 Zeroes` after it.
`6,000,000,000,000,000,000`