Question

If the earth was reduced to the size of an atom how big would the galaxy be?

Answer 1

`x=((1xx10^(-10))(1xx10^21))/12742000=(1xx10^11)/12742000~=7848m~~8km`

Explanation:

We have a ratio question - given the size of the Earth and reducing it to the size of an atom, how big will the galaxy be? That looks like:

`"Earth"/"atom"="galaxy"/x`

So first off we can solve for x:

`x=("atom"xx"galaxy")/"Earth"`

And now we need to make a decision - the size of an atom depends on which atom we're talking about. They typically run between `0.1 to 0.5` nanometres. I'm going to assume we're using a smaller atom (it'll make the math easier).

And now let's get some numbers:

`"Earth"=12,742 km=12,742,000 m`

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=earth+diameter+in+km

`"Atom"= 1 xx 10^-10 m`

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=atom+diameter

`"Galaxy" = 1,000,000,000,000,000,000,000=1xx10^21m`

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=milky+way+diameter+in+km

And now the math:

`x=((1xx10^(-10))(1xx10^21))/12742000=(1xx10^11)/12742000~=7848m~~8km`