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Repeating decimalsRepeating decimals are those rational numbers
These numbers are written by overlining the recurring digit(s) (but here, I underline them because the computer keyboard doesn't allow me to put a line over a number) for example 1/3=0.3333333333333......= 0.3 1/7 = 0.142857142857....= 0.142857 1/9= 0.11111111111......= 0.1 1/11=0.09090909090...= 0.09 Why is 0.9 (repeating) equal to 1?Explanation number 1 Explanation number 3
simple? No! What do you think is 0.9999999999.... (repeating infinitely) equal to? Well that's equal 1! I repeat: 0.9 (repeating) is equal to 1and so al other 9ending recurrent decimals 1.9 = 2 2.9 = 3 3.9 = 4 ..... 567.9 = 568 and so forth. So remember when you use those decimals! Convert them into what they really mean: a whole number, an integer! The confusion is rooted in the fact that we don't have a proper way to represent infinity and hence repeating decimals are approximated in the way above As a result repeating decimals loose "touch" with reality and we don't see anymore that 0.9= 1. The way out is to use fractions, like in explanation 3 of the box above. Click here for an overview diagramm about fractions and decimals
source: http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH070.HTM
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