7.2. Kolya wants to represent the fraction $\frac{3}{7}$ in decimal form, writing down 0 whole numbers and 1000 digits after the decimal point. Then he plans to erase the 500th digit after the decimal point. Will the resulting number be greater or less than $\frac{3}{7}$?
Answer. More. Solution. To answer the question of the problem, it is necessary to find out which is greater: the 500th or the 501st digit after the decimal point? The fraction $\frac{3}{7}$ in decimal form is periodic with a period of 428571 of length 6, that is, $\frac{3}{7}=0.428571428571 \ldots$. Since 500 gives a remainder of 2 when divided by 6, the 500th digit after the decimal point is equal to the second digit in the period, i.e., it is 2, and the 501st digit is the third digit, i.e., 8. Therefore, the obtained number will be greater than the original.