Respuesta :
The 500th digit from 1 to 500 in a row will be;
A: 0 or 1
- We want to write all the whole numbers from 1 to 500 in a row.
- The single digit numbers are; 1 to 9 = 9 numbers = 9 digits
The double digit numbers are; 10 to 99 = 90 numbers × 2 = 180 digits
This is a total of 180 + 9 = 189 digits
- We want to find the 500th digit.
Thus, after 99, we are looking for the;
500 - 189 digit = 311th digit
- 311 is not divisible by 3 and so the nearest term that is divisible by 3 is 312. Thus;
(100 + x)3 = 312
100 + x = 312/3
100 + x = 104
x = 104 - 100
x = 4
- Thus, the 104th term after 99 would contain the 500th digit.
The 104th term after 99 is;
104 + 99 = 203
- Since we used the 312th instead of 311th, it means that 0 is the 311th term.
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As per the question, the 500th digit would be:
a). 0 or 1
To write,
Numbers from [tex]1 to 500[/tex]
The numbers containing 1 digit [tex]= 9[/tex] digits (1 to 9)
The numbers containing 2 digits [tex]= 90[/tex] × [tex]2 = 180[/tex] (from 10 to 99)
To find,
[tex]500th[/tex] digit
Remaining [tex]= 500 - (180 + 9)[/tex]
[tex]= 311th[/tex]
As we know, 311 can not be divided by 3, and therefore, we will look for the nearest number that is divisible by 3 i.e. 312
So, assuming the x as 100 + nth digit
[tex](100 + x)3 = 312[/tex]
[tex]100 + x = 312/3[/tex]
[tex]100 + x = 104[/tex]
[tex]x = 104 - 100[/tex]
∵[tex]x = 4[/tex]
Now,
[tex]100 + 4 = 104th digit[/tex]
∵ [tex]104 + 99 = 203[/tex]
Since the [tex]312th[/tex] term is employed rather than the [tex]311th[/tex], it implies that[tex]203 - 3 = 200[/tex]. Thus, 0 would be the [tex]500th[/tex] digit.
Thus, option a is the correct answer.
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