<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<p><font face="Times New Roman, Times, serif">2^10 is about 1000, so
2^50 would be about (2^10)^5 which is about 1000^5 or 10^15.</font></p>
<p><font face="Times New Roman, Times, serif">A ream of paper is 500
sheets and about 2" high so 1000 sheets would be 4" high so each
sheet is 4*10^-3 high. Multiplying that by 10^15, which is the
number of thicknesses of paper, we get 4*10^12". To convert to
miles, divide by 12*5280, which is a bit more than 5*10^4, so we
get somewhat less than 10^8 miles. An astronomical unit
(Earth-Sun distance) is around 93,000,000 miles (I can still
hear my dad's voice telling me that when I'm still a little kid)
or about 10^8. So the stack of paper would approximately reach
the Sun, way farther than the moon.</font></p>
<p><font face="Times New Roman, Times, serif">Checking my work, the
height of the paper would be</font></p>
<p><font face="Times New Roman, Times, serif">(2**50)*(4*10.0**(-3))/(12*5280)<br>
=> 71079539.57339798</font></p>
<p><font face="Times New Roman, Times, serif">which is indeed the
same order of magnitude as an astronomical unit. Of course the
mass of that folded stack of paper would be so huge that we'd
have crashed into the Sun, or vice versa. So kids, don't try
this at home!<br>
</font></p>
<p>-- <br>
</p>
<p style="font-family: Times, serif">
Jon "Overshoot The Moon" Dreyer<br>
<a href="http://www.passionatelycurious.com">Math Tutor/Computer
Science Tutor</a><br>
<a href="http://music.jondreyer.com">Jon Dreyer Music</a>
</p>
<div class="moz-cite-prefix">On 9/27/23 1:04 PM, Steve Parus via
LCTG wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CA69D5A0-B9F8-4C38-89E8-509485E1CE4F@umich.edu">
<div dir="ltr">The change in diameter is equal to the change in
circumference divided by pi. </div>
<div dir="ltr"><br>
</div>
<div dir="ltr">Another one: if a piece of paper is repeatedly
folded in half 50 times, would its thickness reach the moon?</div>
<div dir="ltr"><br>
</div>
<div dir="ltr">Steve Parus</div>
</blockquote>
<div class="moz-signature"><br>
</div>
</body>
</html>