{"id":81,"date":"2009-04-20T14:30:28","date_gmt":"2009-04-20T02:30:28","guid":{"rendered":"https:\/\/blog.waikato.ac.nz\/physicsstop\/2009\/04\/20\/ninety_eight_ninety_nine_a_hun\/"},"modified":"2009-04-20T14:30:28","modified_gmt":"2009-04-20T02:30:28","slug":"ninety-eight-ninety-nine-a-hun","status":"publish","type":"post","link":"https:\/\/blog.waikato.ac.nz\/physicsstop\/2009\/04\/20\/ninety-eight-ninety-nine-a-hun\/","title":{"rendered":"Ninety Eight, Ninety Nine, A Hundred…"},"content":{"rendered":"

My niece, the one who was interested in reflections<\/a>, is now into maths. She’s recently added the number ‘googol’ into her vocabulary. As in "Uncle Marcus, I’m going to count from one to a googol; one, two, three, four…" – though I’m not convinced she’s actually done it yet.<\/p>\n

A googol (not to be mistaken for google) is a large number, specifically ten to the power one hundred. That is, in our conventional decimal notation, a ‘1’ followed by a hundred ‘0’s. Or:<\/p>\n

10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000.<\/p>\n

<\/p>\n

Easy to write down, but just how big is it? Let’s think about laying one googol atoms end to end; how long would it be. An atom is approximately one angstrom in size, give or take, that’s ten to the power of minus ten, or 0.0000000001 metres. <\/p>\n

We need some big distances, so let’s talk about light years. A light year is the distance light travels in a year. With light travelling at about 300 million metres per second, with about 30 million seconds in a year (365 x 24 x 60 x 60), that gives us about ten to ther power sixteen metres in a light year. If we lay atoms end to end to stretch a light year, we’ll need about ten to the power twenty-six atoms. That’s not much compared to a googol.<\/p>\n

A googol of atoms will stretch ten to the power of 74 light years (100 minus 26). Cosmologists reckon that the observable universe is only about 50 billion light years in size<\/a>. That’s a rather paltry distance compared to our googol of atoms. More to the point, the universe is thought to contain about ten to the power eighty atoms, comfortably less than a googol.<\/p>\n

Given that there are not close to a googol of things to count in this universe, I reckon a googol is a good working approximation to infinity. But if that’s not big enough for you, try a googolplex – that’s a one followed by a googol of zeros. I’d like to hear niece try counting that high.<\/p>\n","protected":false},"excerpt":{"rendered":"

My niece, the one who was interested in reflections, is now into maths. She’s recently added the number ‘googol’ into her vocabulary. As in "Uncle Marcus, I’m going to count from one to a googol; one, two, three, four…" – though I’m not convinced she’s actually done it yet. 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