Processing Math: Done
Solution 1.1:7c
From Förberedande kurs i matematik 1
If we look more closely at this number, we see that the combination 001 is repeated from the second decimal place onwards,
2 001 001 001...and this reveals that the number is rational.
By multiplying a certain number of times by 10 we can move the decimal place step by step to the right.
x=0 2 001 001 001...
10x=2 001 001 001 1...
100x=20 01 001 001 1...
1000x=200 1 001 001 1...
10000x=2001 001 001 1...
In this list, we see that 10x and 10000x have the same decimal expansion, which means that
10000x−10x=2001 001 001 001...−2001 001 001...
=1999. (decimal parts cancel)
As
9990x=1999 
x=99901999.
