If the number next to '7' is written as 10, then in this system, the value of 100 is

Options

A. a)49
B. b)64
C. c)100
D. d)1

Explanation

To solve the problem, we need to determine the value of '100' in a system where the number next to '7' is written as '10'.

### Step-by-Step Solution:

1. **Understanding the given information**:
- We know that in this system, the number next to '7' is represented as '10'. This implies that there is a specific relationship or rule in this number system.

2. **Identifying the pattern**:
- The value of '7' is being represented as '10'. This suggests that the number system might be using a base that is different from the decimal system.
- In a typical base-10 system, '10' represents the value '10'. However, if '7' is represented as '10', it indicates that we might be working in a base-8 system (octal), where the digits range from 0 to 7.

3. **Converting '100' in base-8 to decimal**:
- In base-8, the number '100' can be converted to decimal as follows:
- The first digit (from the right) represents \(8^0\) (which is 1),
- The second digit represents \(8^1\) (which is 8),
- The third digit represents \(8^2\) (which is 64).
- Therefore, the value of '100' in base-8 is calculated as:
\[ 1 \times 8^2 + 0 \times 8^1 + 0 \times 8^0 = 1 \times 64 + 0 + 0 = 64. \]

4. **Conclusion**:
- The value of '100' in this system is '64'.

### Final Answer:
The value of '100' is **64**.