How many times does the number 5 occur in the range of numbers from 1 to 100?

Options

A. 21
B. 22
C. 20
D. 19

Answer

To determine how many times the number 5 occurs in the range of numbers from 1 to 100, we can break down the occurrences into two parts: the occurrences of 5 in the units place and the occurrences of 5 in the tens place.

### Step-by-Step Solution:

1. **Count occurrences of 5 in the units place:**
- The numbers that have 5 in the units place from 1 to 100 are:
- 5, 15, 25, 35, 45, 55, 65, 75, 85, 95
- There are a total of **10 occurrences** of the number 5 in the units place.

2. **Count occurrences of 5 in the tens place:**
- The numbers that have 5 in the tens place from 1 to 100 are:
- 50, 51, 52, 53, 54, 55, 56, 57, 58, 59
- There are a total of **10 occurrences** of the number 5 in the tens place.
- Note that the number 55 has already been counted in the units place, but we will count it separately here.

3. **Combine the counts:**
- From the units place, we have 10 occurrences.
- From the tens place, we have 10 occurrences.
- Total occurrences = 10 (units) + 10 (tens) = **20 occurrences**.

### Final Answer:
The number 5 occurs **20 times** in the range of numbers from 1 to 100.

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