Why AI Struggles to Compare Numbers like 9.11 and 9.8

Artificial intelligence systems, like ChatGPT, have become powerful tools for processing and understanding natural language. Yet, when it comes to comparing certain numbers—such as 9.11 and 9.8—AI can sometimes make mistakes.

For example, ChatGPT might provide a wrong answer like this:

Wrong answer:
9.11 is bigger than 9.8.
If you compare the numbers place by place, starting from the left:
The whole number part is 9 for both.
In the decimal part, 11 (from 9.11) is larger than 8 (from 9.8).
Thus, 9.11 is greater than 9.8.

This error happens because the AI may interpret numbers as strings of characters instead of actual numeric values. But when the AI is explicitly asked to treat the numbers as numeric data, it can produce the correct result, as shown here:

Correct example:
The number 9.11 is smaller than 9.8.
Even though 11 is larger than 8 when you look at the decimals, 9.8 is the same as 9.80 when comparing with 9.11. In this case, 80 is larger than 11, so 9.8 is bigger than 9.11.

In this article, we'll explore why AI struggles with comparing numbers, especially when they are treated as strings, and how different contexts can lead to different results.

The Difference Between Numbers and Strings

One of the main reasons AI can make errors when comparing numbers is due to how it interprets numbers as strings. In programming, a number can either be treated as a numeric value (such as an integer or floating-point number) or as a string of characters (like text). The problem arises when AI treats numbers like text strings instead of as numeric data.

To understand this, let’s break down what happens when AI compares 9.11 and 9.8 both as numbers and as strings:

1. Numeric Comparison (What Should Happen):

   • When treated as numbers, 9.11 and 9.8 are compared based on their actual values.
   • 9.8 can be seen as 9.80 for easier comparison. Since 80 is greater than 11, 9.8 is larger than 9.11.

2. String Comparison (What Happens in the Error):

   • If the AI interprets these numbers as strings, it compares them character by character, just like it would compare words.
   • In this case, both strings start with '9'. The next comparison is between "11" from 9.11 and "8" from 9.8. Since "11" is lexicographically larger than "8", the AI might wrongly conclude that 9.11 is larger than 9.8.

This string-based logic is where the error originates, leading the AI to make a wrong comparison.

Why Does This Happen?

AI systems like ChatGPT are primarily designed to process and understand natural language. While they are capable of performing basic mathematical functions, their core purpose is interpreting text-based input. Several factors can lead to the AI misinterpreting numbers as strings, causing the kind of mistake seen in the first example.

1. Training on Text Data

AI models like ChatGPT are trained on large datasets consisting mostly of text. These datasets include numbers, but they are often presented within sentences or explanations, not in a strict mathematical context. For example, a sentence might say, “I worked for 9.11 hours,” which is not the same as asking the AI to perform a direct mathematical comparison.

Since the AI is more accustomed to processing numbers as part of text, it might default to treating them as strings in some cases, especially if the context isn’t clear.

2. Contextual Ambiguity

If a question is presented in a way that’s vague or ambiguous, the AI might interpret it incorrectly. For instance, when asked, “Which is bigger: 9.11 or 9.8?”, the AI might treat the numbers as strings unless it is explicitly told to compare them numerically.

In the incorrect example, ChatGPT treats "9.11" and "9.8" like text strings, leading to a lexicographical comparison. In contrast, in the correct example, the user clearly specifies that these are numbers, so ChatGPT switches to numerical reasoning.

3. Inconsistent Input Handling

When the input is clear, like in the correct example where the user specifically asks for a numerical comparison, the AI can correctly handle the task. But when the input is less clear, as in the wrong example, the AI might default to string-based logic.

This inconsistency arises because ChatGPT is a language model first, not a dedicated mathematical tool. It can switch between contexts but might misinterpret them if the prompt isn't specific enough.

String vs. Numeric Comparisons: A Closer Look

The difference between string and numeric comparisons is crucial in understanding this issue:

• Numeric Comparison: When numbers are compared mathematically, the decimal points are treated as part of the value, and the comparison is based on magnitude. For example, 9.8 is equivalent to 9.80, which is larger than 9.11 because 80 is greater than 11.

• String Comparison: When numbers are treated as strings, the system compares them character by character, similar to how it would compare words. In this case, "9.11" and "9.8" are compared starting with the first character. Since both start with "9", the next characters are compared: "11" vs. "8". The system might conclude that "11" is greater than "8", leading to the wrong conclusion that 9.11 is larger than 9.8.

This is why AI, when processing numbers as strings, can make errors that seem obvious to a human but are difficult for a machine to avoid without clear instructions.

How AI Can Be Improved

There are several ways AI systems like ChatGPT could be enhanced to reduce these kinds of errors:

1. Improved Numeric Recognition:

   • AI could be trained to better recognize when numbers are being used in a mathematical context. This would involve more sophisticated pattern recognition to detect numbers and handle them as numeric data by default unless otherwise specified.

2. Clearer Prompts from Users:

   • Users can help avoid errors by being more specific in their prompts. For example, asking “Number 9.11 and number 9.8, which is bigger?” provides clearer input that encourages the AI to interpret the values correctly.

3. Built-in Mathematical Tools:

   • AI systems could integrate more robust mathematical functions that automatically handle numeric comparisons, ensuring that numbers are processed correctly even when the context is somewhat ambiguous.

4. Error-Handling Mechanisms:

   • The AI could be equipped with mechanisms to double-check numerical comparisons, prompting the user for clarification if there is ambiguity between treating input as numbers or strings.

AI systems sometimes struggle to compare numbers like 9.11 and 9.8 because they can interpret numbers as strings rather than numeric values. This leads to errors, like the AI concluding that 9.11 is larger than 9.8 based on character-by-character comparison. When explicitly told to treat the input as numbers, the AI can provide the correct result, as shown in the correct example.

To improve accuracy, AI models need better tools for recognizing and handling numeric data, and users can also help by providing clearer prompts. As AI continues to develop, addressing these issues will be important for ensuring that systems like ChatGPT can handle not only language but also precise mathematical tasks.