Written by David Newman
• 5/3/2023
• Read Time : 3 min.

# ChatGPT versus PTC Mathcad: Units, Reliability, and Rounding

## The Problem

Recently, a colleague from Europe asked American teammates how to express the dimensions 3’ 1/8” x 3’ 1/8 (a 36.125-inch square) in centimeters. She explained that American metrics made her lost. It was a very simple unit conversion ask. The answer is 91.7575 cm x 91.7575 cm.

## ChatGPT Try 1

Another colleague took to ChatGPT, the viral artificial intelligence (AI) chatbot, to produce an answer to this simple question. This was the output he received:

"3 feet and 1/8 inch is equivalent to 93.98 cm, and 3 feet and 1/8 inch is equivalent to 93.98 cm as well. Therefore, the dimensions in cm are: 93.98 cm x 93.98cm.”

ChatGPT’s confident tone in its first response led both of my colleagues to believe 93.98 cm was correct. However, 36.125 inches being equivalent to 93.98 centimeters assumes a conversion rate of 2.6015 centimeters for one inch. This is factually wrong, and ChatGPT made the same conversion error twice in one sentence. One inch is equal to 2.54 centimeters. I noted my colleague’s use of ChatGPT and its incorrect response.

## ChatGPT Try 2

As a big believer in ChatGPT’s prowess and usefulness, my colleague asked ChatGPT to modify the answer:

"That’s wrong...recalculate that"
“I apologize for the mistake in my previous answer. The correct conversion of 3 feet and 1/8 inch is approximately 93.66 cm, and the same applies for the other dimension of 3 feet and 1/8 inch. Converting both dimensions to centimeters, we get: 93.66 cm x 93.66 cm. I hope this helps!”

Unfortunately, ChatGPT’s second try does not help. With 93.66 cm, ChatGPT now believes that the conversion ratio of one inch to centimeters is 2.5923 centimeters per inch. That’s still incorrect.

In try two, ChatGPT can recognize that it made a mistake, but that begs the question of why it’s giving out faulty information in the first place? It then gave out another mistaken answer as a correction. Clearly, ChatGPT doesn’t know what the mistake it made was to begin with. I wouldn’t count on AI taking over engineering calculations any time soon.

## ChatGPT Try 3

My colleague believed that the third time would be the charm and rephrased the question to:

“What is 3 feet and 1.8 inchs in centimeters?”
“3 feet and 1/8 inch is approximately equal to 93.6775 centimeters. To convert, we first need to find the total of inches. 3 feet = 36 inches; 1/8 inch = 0.125 inches. So 3 feet and 1/8 inch is equal to 36.125 inches.
Next, we can convert inches to centimeters by multiplying by 2.54: 36.125 inches *2.54 cm/inch = 91.7675 cm
Rounding this to the nearest hundredth gives us 93.68 cm, but if you only need one decimal place, the answer would be 93.7 cm.”

With this third bizarre response, my colleague finally admitted that his “confidence in ChatGPT JUST DIED!” Remember, ChatGPT has now provided four different answers to the same problem: 93.98 cm, 93.66 cm, and now both 91.7675 cm and 93.6775 cm in the same answer. All of those are wrong. In the end, ChatGPT never provided the correct answer of 91.7575 cm.

ChatGPT is correct that 3 feet and 1/8 inches is 36.125 inches. ChatGPT is also (finally) correct that the conversion rate is 2.54 cm/inch. However, ChatGPT is incorrect that 36.125 inches * 2.54 cm/inch= 91.7675 cm. (Remember, it’s 91.7575 cm.)

But ChatGPT totally goes off the rails when it tries to “round to the nearest hundredth” and to the nearest tenth, even though it wasn’t prompted to do so. And it appears to use this new, rounded answer as the basis of its 93.6775-centimeter answer. Apparently, 91.7675 rounded to two decimal places is 93.68. This is wrong on both sides of the decimal place. What a mess.

## PTC Mathcad Prime: Only One Try Needed

It’s time for us to turn to a real math software: PTC Mathcad Prime. Unlike ChatGPT or even Excel spreadsheets, Mathcad Prime is unit-aware and balances units. It has unit conversion ratios built in, and you can rely on Mathcad Prime to give you the correct result the first time, as tens of thousands of businesses and universities already do today.

Unlike with ChatGPT, if you recalculate the same Mathcad Prime worksheet multiple times, you’ll get the same consistent, correct response every time.

PTC Mathcad Prime doing the unit conversions and rounding that ChatGPT tried but failed at doing.

Mathcad knows that 2.54 centimeters goes into one inch, and it knows that three feet plus 1/8 of an inch is 36.125 inches. Mathcad knows that can be converted to 91.7575 centimeters, and it will display the length in centimeters just by changing which unit is at the end of the expression, whether it’s inches or centimeters.

Mathcad customers often express how useful it is to work with a purpose-built engineering and mathematics software that recognizes units, including the potential to catch errors if there is a unit mismatch. With Mathcad Prime, the software catches your errors and provides clear feedback on what those errors are—a world of difference compared to my colleague having to plead with ChatGPT to stop making errors.

With regards to rounding numbers, in Mathcad, you can change the Display Precision of a math expression in the Math Formatting tab, which will change the decimal places displayed in the results if you want only one or two decimals. Display Precision doesn’t affect the accuracy of the results if you perform further calculations. If you do want to affect future result precision by rounding the result, you can use Mathcad Prime’s built-in rounding and truncation functions to do so, shown in the screenshot above.

Our customers often rave about Mathcad’s document-oriented approach and natural math notation, making it easy for their stakeholders to read through a Mathcad worksheet and understand every step of the process. The same can’t be said for “black box” kinds of software, like an Excel formula with several cell references, or ChatGPT with whatever process it used to come up with four uniquely wrong answers.

Use software for the purpose it was built for!