Counting the Occurrences of Digit 5 from 1 to 10000

Calculating the exact number of times a specific digit appears in a range of numbers can be an intriguing and challenging problem. This article examines how many times the digit 5 is written when writing all numbers from 1 to 10000, providing a detailed breakdown of the counting process.

Breakdown by Digit Place

The digit 5 can be found in different positions within numbers. We will analyze each digit place separately: units, tens, hundreds, and thousands.

Units Place

In every set of 10 numbers (e.g., 0000-0009, 0010-0019, etc.), the digit 5 appears once in the units place. To find the total occurrences of 5 in the units place from 1 to 10000, we consider:

There are 1000 complete sets of 10 in 10000. Thus, the digit 5 appears 1000 times in the units place.

Tens Place

Similar to the units place, in every set of 100 numbers (e.g., 0000-0099, 0100-0199, etc.), the digit 5 appears 10 times in the tens place (e.g., 0050-0059, 0150-0159, etc.). Calculating the total occurrences of 5 in the tens place:

There are 100 complete sets of 100 in 10000. Hence, the digit 5 appears 1000 times in the tens place.

Hundreds Place

For every set of 1000 numbers (e.g., 0000-0999, 1000-1999, etc.), the digit 5 appears in the hundreds place for 100 consecutive numbers (e.g., 0500-0599, 1500-1599, etc.). The total occurrences of 5 in the hundreds place can be calculated as follows:

There are 10 complete sets of 1000 in 10000. Thus, the digit 5 appears 1000 times in the hundreds place.

Thousands Place

The digit 5 can only appear in the thousands place in the range from 5000 to 5999, which consists of 1000 numbers. Hence, the total occurrences of 5 in the thousands place are:

The digit 5 appears 1000 times in the thousands place.

Total Count

Summing up the occurrences from all digit places to find the total number of times the digit 5 is written:

Units place: 1000 Tens place: 1000 Hundreds place: 1000

Total occurrences of 5 1000 1000 1000 1000 4000

Therefore, the digit 5 is written 4000 times when writing all numbers from 1 to 10000.

Related Content

This problem involves counting and digit analysis, which are fundamental concepts in number theory and can be useful in various mathematical and computational contexts. Understanding such patterns can help improve SEO by ensuring content is relevant, informative, and structured for search engines.

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