Fractions and MeasurementDate: 04/11/97 at 12:11:09 From: Ed Stanley Subject: Fractions and Measurement We are studying measurement in school and I have noticed there is nothing smaller than an inch with a name unlike 1/2, 1/4,and 1/8 inch. Are there any names? Can you give me a list of fractions until .0000000---until 51 zeros? Date: 04/11/97 at 15:12:55 From: Doctor Steven Subject: Re: Fractions and Measurement Rational numbers are infinite in number; there are an infinite number of them between any two points. Take the fractions between 0 and 1 for instance we have : 1/1, 1/2, 1/3, 1/4, .... We can keep going on forever and we will still have more to count. On a ruler, we tend to use powers of 2 in the denominator: 1/2^1 = 1/2 = 0.5 1/2^2 = 1/4 = 0.25 1/2^3 = 1/8 = 0.125 1/2^4 = 1/16 = 0.0625 1/2^5 = 1/32 = 0.03125 1/2^6 = 1/62 = 0.015625 1/2^7 = 1/128 = 0.0078125 Each time we increase the exponent by about 3, we add another decimal place, more or less. So we'd have to get up to about 1/2^150 to get 50 zeros in front of the decimal place. We would never use fractions this small, so we don't give them names. However, there are some traditional units that are smaller than an inch. At one of our favorite sites about units, How Many? A Dictionary of Units http://www.unc.edu/~rowlett/units/ we find the 'line': line (li) [1] a traditional unit of distance equal to 1/12 inch (about 2.1167 millimeters). For measuring the thickness of buttons, there is also a smaller line equal to 1/40 inch (0.635 millimeter). The line is called the ligne (see above) in French, the linea in Spanish, the linie in German, and the liniya in Russian. line [3] a unit of distance equal to 1/14 inch, used in printing and advertising. This usage is short for agate line. You can also find there descriptions of units called 'points' and 'picas', which are used by printers. Hope this helps! -Doctor Steven, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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