Repeating 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)
1/7 = 0.142857142857....= 0.142857
1/9= 0.11111111111......= 0.1
Why is 0.9 (repeating) equal to 1?
Explanation number 1
Explanation number 3
What do you think is 0.9999999999.... (repeating infinitely) equal to?
Well that's equal 1!
0.9 (repeating) is equal to 1
and so al other 9-ending 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
from repeating decimals back to the homepage
On the shore of a vast sea
Stay in touch with nature. It's full of mathematics!
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