Let A = 1/1.00...001 (there are 99 zeros in the expression). Convert A in decimal number and describe the pattern after the decimal point.
5 point 11
10 for I=1 to 22
20 R=1+10^(-I)
30 A=1/R
40 print I,A/1
50 next
finds that when I = 1, i.e., (A=1/1.1), the pattern after 0. is 90909090...
When I = 2, that is A=1/1.01, the value of A is 0.99009900990099...
The number of 9's in a row is I and the number of 0's in a row is I and the pattern repeats, where I is one more than the number of zeros in the original expression.
When there are 99 zeros in the expression, I = 100, so the decimal point is followed by 100 9's and then 100 zeros, and these sets repeat forever.
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Posted by Charlie
on 2019-07-12 12:09:54 |
computer-aided solution
