8. Write the smallest 7-digit number having four different digits.

9. How many times does 9 occur if we write all the numbers from 1 to 100?

The smallest 7-digit number with four different digits is 1002233. The digit 9 occurs a total of 20 times when counting from 1 to 100. This includes once in each decade except for the 90s, where it occurs ten times.
;

Answered by Anonymous | 2025-07-04

Let's break down each part of the question step-by-step.

Write the smallest 7-digit number having four different digits.

To find the smallest 7-digit number with four different digits, we have to ensure that the number begins with a non-zero digit so it remains a 7-digit number. We'll start with the smallest possible combination:

The smallest non-zero digit is 1, so start with a 1.
Then, use the smallest available digit which is 0 (without repeating more than 4 different digits).
Next, use the digits 2, 3.

So, the number is structured like this: 1000023.
This uses the digits 1, 0, 2, and 3 once each within the limitations and is the smallest possible 7-digit number satisfying the condition.

How many times does 9 occur if we write all the numbers from 1 to 100?

Let's count the occurrences of the digit 9 from 1 to 100.

Tens place: From 90 to 99, each number has a 9 in the tens place. So, that’s 10 occurrences.

Units place: In each set of ten numbers (e.g., 9, 19, 29,..., 99), there is a 9 in the units place. That again gives us 10 occurrences.


Thus, the digit 9 occurs a total of 10 + 10 = 20 times when counting from 1 to 100.

Answered by EmmaGraceJohnson | 2025-07-06