4
The digit 1 appears 301 times, as opposed to 300 for the digits 2 to 9.
The digit '6' appears most often (two times). The other digits only appear once.
A significant figure is the number of digits to the left of the decimal place from the right most non zero digit to the left most digit, or the number of digits from the right most digit to the right of the decimal place to the left most digit. So, 5748 to two significant digits is 5700
Pi is a never ending number, so the digit that appears most often could be anything, based on how long you let the number go out to. If you let Pi go out to 11 digits, the answer is 5. 3.1415926535... But if you let Pi go out to 25 digits, the numbers 4, 5, and 6 are tied. 3.14159265358979323846264...
For a 3 digit number, the left most or the most significant digit cannot be zero. So it can be 1,2,3,4,5,6,7,8 or 9 which is 9 possibilities. The middle number can be 0,1,2,3,4,5,6,7,8,9 which is 10 possibilties but one of the digits has been chosen already as the first digit, so the possibilities are only 9. The right most number can be 0,1,2,3,4,5,6,7,8,9 which is 10 possibilities but two of the digits have been already used by the left most and the middle digits. That leaves only 8 possibilities. So the total number of three digit numbers that have three distinct digits is 9 x 9 x 8 = 81 x 8 = 648 possibilities
say your first decimal is 0.114 and the second 0.116 the first and second is 11/100 in both examples and appear the same; if you go to third (different) digit the first is 114/1000 and the second is 116/1000 so you can now see the difference
According to Benford's law, the first digit is most likely to be 1. Benford's law for the first digit states that the probability of digit, d, is log10(1 + 1/d) where d = 1, 2, ... , 9. [0 cannot be the leading digit]. This gives the probability of 1 as 30.1%. The distribution becomes more uniform as the number of digits in the representation of numbers is increased but since we usually truncate numbers to a few digits, the state of uniformity is not always reached.
Mental math like if 12 into 72 it will not be a double digit if you divide 100 by 10 it will be double digits. Most times if you have a tripple digit number and divide it by double digit the answer will be a double digit.
The biggest 4 digit number that can be made from using the digits of 850236, using a digit at most once, is 8653.
102345 is the smallest [positive] 6-digit number with no repeats.
For this type of "the largest number which..." questions, you need to advance from left to right, using the largest possible digit in each case. For the first two digits, that would be 9, for the third digit (the right-most digit), the largest digit which will make this possible is an 8.
25 & 36.