How many times does the digit 8 appear in number from 1 to 100? What fraction of number up to 100 has number 8 present in them?

Answer

To solve the problem of how many times the digit 8 appears in numbers from 1 to 100 and what fraction of those numbers contain the digit 8, we can follow these steps:

### Step 1: Count occurrences of the digit 8 from 1 to 100

1. **From 1 to 10**: The digit 8 appears **1 time** (in the number 8).
2. **From 11 to 20**: The digit 8 appears **1 time** (in the number 18).
3. **From 21 to 30**: The digit 8 appears **1 time** (in the number 28).
4. **From 31 to 40**: The digit 8 appears **1 time** (in the number 38).
5. **From 41 to 50**: The digit 8 appears **1 time** (in the number 48).
6. **From 51 to 60**: The digit 8 appears **1 time** (in the number 58).
7. **From 61 to 70**: The digit 8 appears **1 time** (in the number 68).
8. **From 71 to 80**: The digit 8 appears **2 times** (in the numbers 78 and 80).
9. **From 81 to 90**: The digit 8 appears **10 times** (in the numbers 81, 82, 83, 84, 85, 86, 87, 88, 89, and 88).
10. **From 91 to 100**: The digit 8 appears **1 time** (in the number 98).

### Step 2: Calculate the total occurrences

Now, we can add up all the occurrences:
- From 1 to 10: 1
- From 11 to 20: 1
- From 21 to 30: 1
- From 31 to 40: 1
- From 41 to 50: 1
- From 51 to 60: 1
- From 61 to 70: 1
- From 71 to 80: 2
- From 81 to 90: 10
- From 91 to 100: 1

**Total occurrences of the digit 8 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 10 + 1 = 20 times.**

### Step 3: Calculate the fraction of numbers containing the digit 8

To find the fraction of numbers that contain the digit 8:
- The total number of occurrences of the digit 8 is 20.
- The total numbers from 1 to 100 is 100.

The fraction is:
\[ \text{Fraction} = \frac{\text{Total occurrences of 8}}{\text{Total numbers}} = \frac{20}{100} = \frac{2}{10} = \frac{1}{5} \]

### Final Answer
- The digit 8 appears **20 times** in numbers from 1 to 100.
- The fraction of numbers up to 100 that contain the digit 8 is **\(\frac{1}{5}\)**.

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