Answer :
- Multiply $2222222222222$ by $11$, which equals $24444444444442$.
- Count the number of 4s in the result.
- There are thirteen 4s in $24444444444442$.
- The number of 4s is $\boxed{13}$.
### Explanation
1. Problem Analysis
We are asked to find the number of 4s in the product of $2222222222222 \times 11$. First, we need to calculate the product.
2. Multiplication Setup
Let's multiply $2222222222222$ by $11$. We can rewrite this as $2222222222222 \times (10 + 1)$. This equals $22222222222220 + 2222222222222$.
3. Performing the Addition
Adding these two numbers, we get:
$22222222222220 + 2222222222222 = 24444444444442$.
4. Counting the 4s
Now, we need to count the number of 4s in the result $24444444444442$. By counting, we can see that there are thirteen 4s.
5. Final Answer
Therefore, the number of 4s in the product is $\boxed{13}$.
### Examples
Understanding how digits repeat in multiplication can help in cryptography when analyzing patterns in large numbers. For instance, if you're encoding a message and multiplying a repeating sequence by a constant, recognizing the resulting digit patterns can help in both creating and breaking codes. This is particularly useful in simplifying complex calculations and identifying vulnerabilities in encryption methods.
- Count the number of 4s in the result.
- There are thirteen 4s in $24444444444442$.
- The number of 4s is $\boxed{13}$.
### Explanation
1. Problem Analysis
We are asked to find the number of 4s in the product of $2222222222222 \times 11$. First, we need to calculate the product.
2. Multiplication Setup
Let's multiply $2222222222222$ by $11$. We can rewrite this as $2222222222222 \times (10 + 1)$. This equals $22222222222220 + 2222222222222$.
3. Performing the Addition
Adding these two numbers, we get:
$22222222222220 + 2222222222222 = 24444444444442$.
4. Counting the 4s
Now, we need to count the number of 4s in the result $24444444444442$. By counting, we can see that there are thirteen 4s.
5. Final Answer
Therefore, the number of 4s in the product is $\boxed{13}$.
### Examples
Understanding how digits repeat in multiplication can help in cryptography when analyzing patterns in large numbers. For instance, if you're encoding a message and multiplying a repeating sequence by a constant, recognizing the resulting digit patterns can help in both creating and breaking codes. This is particularly useful in simplifying complex calculations and identifying vulnerabilities in encryption methods.
