If you write down all the numbers from 1 to 100, then how many times do you write 3 ?Options18112021

1. Break Down the Problem

We need to count how many times the digit '3' appears in the numbers from 1 to 100. This can occur in the tens place or the units place.

2. Relevant Concepts

We will analyze two ranges:

• Numbers 1 to 9
• Numbers 10 to 99
• The number 100 contains no '3'.

3. Analysis and Detail

Step 1: Count occurrences from 1 to 9

• The digit '3' appears once: (3).

Occurrences from 1 to 9: 1 time

Step 2: Count occurrences from 10 to 99

• In the tens place:

  • 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 (10 occurrences)

• In the units place:

  • 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 (10 occurrences)

Occurrences from 10 to 99:

• Tens place: 10 occurrences.
• Units place: 10 occurrences.

Total for 10 to 99: $10 + 10 = 20$.

Step 3: Count occurrences in 100

• The number 100 does not contain the digit '3'.

4. Verify and Summarize

• Occurrences from 1 to 9: 1
• Occurrences from 10 to 99: 20
• Occurrences in 100: 0

Total occurrences of the digit '3' in the numbers from 1 to 100: $1 + 20 + 0 = 21$

Final Answer

The digit '3' is written 21 times when writing all the numbers from 1 to 100.