Question

Можете помочь пожалуйста, с объяснением Все натуральные числа, начиная с еденицы, выписаны подряд без пробелов и запятых. Какая цифра стоит на 2022 месте?​

Answer 1

Ответ: 0

Пошаговое объяснение:

Количество n-значных чисел определятся по формуле:

N(n) = (10^n -1) - (10^(n-1) - 1) = 10^(n-1)*(10 -1 ) = 9*10^(n-1)

Например:

Однозначных: 9

Двузначных: 90

Трехзначных: 900

и т.д.

Заметим, что  9 + 2*90<2022, а 9 +2*90 + 3*900>2022, откуда легко сделать вывод, что последнее число в слитном ряду является трехзначным.

Определим порядковый номер этого последнего трехзначного числа начиная со 100 (1-е трехзначное число):

( 2022 - 9 - 90*2)/3 = 1833/3 = 611

611-е трехзначное число это число  100 + 611 -1 = 710, а значит на 2022 месте стоит цифра 0.

Answer 2

The digit at the 2022nd place in the sequence of natural numbers

To find the digit at the 2022nd place in the sequence of natural numbers, we can analyze the pattern and use some basic math.

The sequence of natural numbers starts with 1, 2, 3, 4, and so on. We can observe that the number of digits in each number increases as we move forward in the sequence.

To determine the digit at the 2022nd place, we need to find the range of numbers that precede it. Let's break it down:

- Numbers 1 to 9: These are single-digit numbers, and there are 9 of them. - Numbers 10 to 99: These are two-digit numbers, and there are 90 of them (10 to 99). - Numbers 100 to 999: These are three-digit numbers, and there are 900 of them (100 to 999). - Numbers 1000 to 9999: These are four-digit numbers, and there are 9000 of them (1000 to 9999).

By adding up the counts of the numbers in each range, we can determine the total number of digits that precede the 2022nd place.

- Total digits in the single-digit range: 9 * 1 = 9 - Total digits in the two-digit range: 90 * 2 = 180 - Total digits in the three-digit range: 900 * 3 = 2700 - Total digits in the four-digit range: 9000 * 4 = 36000

Now, let's calculate the remaining digits after the four-digit range:

- Remaining digits: 2022 - (9 + 180 + 2700 + 36000) = 2022 - 38989 = 16933

From the calculation above, we know that the digit at the 2022nd place is located in the five-digit number range.

- Numbers 10000 to 99999: These are five-digit numbers, and there are 90000 of them (10000 to 99999).

To find the specific digit at the 2022nd place, we can divide the remaining digits (16933) by the number of digits in each number (5) and determine the position within the number.

- Position within the number: 16933 / 5 = 3386 remainder 3

Since the remainder is 3, the digit at the 2022nd place is the 3rd digit of the 3386th five-digit number.

To find the actual number and its digit, we can calculate:

- The 3386th five-digit number: 10000 + 3386 - 1 = 13385 - The 3rd digit of the number 13385: 3

Therefore, the digit at the 2022nd place in the sequence of natural numbers is 3.