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

1 Answer

#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#