Question

How many times does the digit 9 appear in the counting numbers from 1 to 99?

Answer 1

In the counting of numbers from 2 to 99, the digit 9 appears 20 times.

Listing the Numbers

To identify how many times the digit 9 appears, we can first list the numbers we know have a 9 in them:

9, 19, 29, 39, 49, 59, 69, 79, 89, 99

Although we've identified these numbers, we are not finished. Numbers in the 90s also qualify as digits of 9. Therefore, these numbers also are included:

91, 92, 93, 94, 95, 96, 97, 98

Answer Recap

Now that we have all the numbers from 1 to 99 with the digit 9 in them, we can count up how many numbers there are with consideration that the number 99 also has two digits of 9 in it:

[(10 + 8) + 2] = 20

Hence, the digit 9 appears 20 times in the counting numbers from 1 to 99.

Answer 2

There are 20 times the digit 9 appears in counting numbers from 1 to 99.

Explanation:

To see why this is the case, we can break the counting numbers down into two categories: numbers with a 9 in the units place and numbers without a 9 in the units place.

For the first category, we can count the number of times a 9 appears in the units place by counting from 9 to 99 in increments of 10. There are 10 numbers in this category.

For the second category, we can count the number of times a 9 appears in the tens place by counting from 19 to 99 in increments of 100. There are 10 numbers in this category as well.

Therefore, the total number of times the digit 9 appears in counting numbers from 1 to 99 is 20 times.