Solving 10/10 10/10 10/10 and the Mystery of 1010101010

Introduction to the Problem

What is the answer to 10/10 10/10 10/10? A common belief is that this equals 1 1 1 which totals to 3. However, is this the complete truth?

Understanding the Solution through Basic Arithmetic

Taking a closer look at the operation, we see that all the numerators (ones place values) are zeros. In arithmetic, when multiplying by zero, the result is always zero (10 0). Therefore, the answer will end with a zero.

The tens place values are all ones, so we must add up 1 1 1 1. This gives us 4. Adding a zero at the end of this sum, we conclude that the final answer is 40.

This can also be achieved using multiplication. The expression can be rewritten as 10 x 4, resulting in 40. Or, you could apply the same mechanism as above, calculating 4 x 1, and then adding a zero at the end, again leading to the answer 40.

PEMDAS Approach to the Equation

According to the order of operations (PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction), the first step is to perform 10/10, which equals 1. Then we must address 101. The number 101 represents 11 in decimal (binary 101 5, but in the context of this problem, it is treated as 11).

Putting these together, we get 1 11 12. Since the problem is structured similarly to the first example, we can apply the same strategy to get the total of 40.

Another Mystery: 1010101010

Interestingly, another variant of the problem is: 1010101010. The answer to this equation is 50. Here’s how:

When you interpret 1010101010 as a binary number, it translates to 524 in decimal (10101010102 52410). But if we consider it as a base-10 number with each digit representing a place value, the arithmetic is the same as the previous problem. So, 1010101010 50.

However, it’s important to note that this interpretation varies based on the context. In mathematical puzzles or logical games, 1010101010 can be interpreted in different ways, leading to a variety of answers based on the problem’s structure.

Conclusion

While the problem 10/10 10/10 10/10 might seem straightforward, the answer is not always as simple as it appears. By methodically applying the order of operations and basic arithmetic principles, we can arrive at a more accurate response. Similarly, for 1010101010, understanding the context and rules of interpretation is crucial in solving such puzzles effectively.