tag:blogger.com,1999:blog-5303307482158922565.post3735307741590515601..comments2024-07-23T09:12:20.588-07:00Comments on Math Mama Writes...: Carnival of Mathematics #56Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-5303307482158922565.post-12497939872877465182009-08-30T08:50:15.099-07:002009-08-30T08:50:15.099-07:00Good line of thought, but as you found out, the &q...Good line of thought, but as you found out, the "subtract largest power of two" method is a lot uglier for fractions than whole numbers.<br /><br />The simple method is "repeated multiplication by 2":<br /><br />0.1 * 2 = 0.2<br />0.2 * 2 = 0.4<br />0.4 * 2 = 0.8<br />0.8 * 2 = 1.6<br />0.6 * 2 = 1.2<br />0.2 * 2 ... repeats<br /><br />The answer is the integral parts of the products, which are subtracted out along the way: 0.00011..., or to use my repeating notation, 0.0(0011).Rick Reganhttp://www.exploringbinary.com/noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-34688026547786043232009-08-30T06:27:17.488-07:002009-08-30T06:27:17.488-07:00Hmm, I'm wondering if there's any easy way...Hmm, I'm wondering if there's any easy way to do the conversion process. I tried working on 1/10, and it seemed hideous. <br /><br />I said (to myself) 1/10 is smaller than 1/2, 1/4, and 1/8, so there are 3 leading 0s. It's bigger than 1/16, so we have a 1 now, and I have to find 1/10-1/16. That equals 3/80, which is bigger than 1/32, so we get another 1, and need to find 3/80-1/32. That comes out more nicely than I expected, to 1/160.<br /><br />I wasn't seeing any pattern and stopped that. Went to Wolphram alpha. Yep, I see .99, as you say, has 20 digits in its repeating pattern. But .9 only has 4. Hmm...Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-66766049357913167342009-08-29T17:18:44.160-07:002009-08-29T17:18:44.160-07:00Most decimal fractions are infinite repeating in b...Most decimal fractions are infinite repeating in binary. 0.99 is 0.11(11110101110000101000), where the part in parentheses is repeating.<br /><br />You can play with these yourself. I've written a converter that can be found at: http://www.exploringbinary.com/binary-converter/ (it doesn't mark the repeating part -- you'll have to infer that yourself).Rick Reganhttp://www.exploringbinary.com/noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-65828821195116685062009-08-29T16:11:09.466-07:002009-08-29T16:11:09.466-07:00(edited to fix the confusing wording)(edited to fix the confusing wording)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-16619434737369873042009-08-29T12:36:20.798-07:002009-08-29T12:36:20.798-07:00Good point. I meant numbers in the decimal system,...Good point. I meant numbers in the decimal system, but it's not clear. I wonder what decimal fractions (like .99) would look like as binary fractions.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-91939049246110353642009-08-29T10:53:29.473-07:002009-08-29T10:53:29.473-07:00Sue -- just one quibble with your wording "on...Sue -- just one quibble with your wording "on decimals like 999...". I talk about integers written in decimal (AKA base 10), not decimals as in decimal fractions. <br /><br />(And BTW, thanks for mentioning my article.)Rick Reganhttp://www.exploringbinary.com/noreply@blogger.com