Hello,

I am studying for my CQT exam which is rapidly approaching. I hit a snag on a practice exam question and I am not getting sufficient clarification from the ASQ help desk via e-mail. They directed me here for further inquiry, I'd appreciate any input on this issue.

Question: Truncate the following number to four significant digits

7.4688523

a) 7.4688

b) 7.469

c) 7.468

d) 7.4689

I selected c, as it is truncated, not rounded, and contains four significant digits.

The answer key popped up incorrect, and instructed that a) 7.4688 was the correct answer.

The review blurb said “7.4688 is correct. It has four significant digits”

The help desk forwarded me an e-mail response from the Learning Team that said my mistake was that I was rounding (which is incorrect, the rounding error would have been selecting asnwers b or d), and then provided an example of a truncation calculator with the criteria “Truncate 7.4688523 to 4 decimal places” and the output was 7.4688. This is incredibly frustrating, because the original question did not ask for the number to be truncated to 4 decimal places, it asked for the answer to be truncated to four significant digits. 7.4688 contains 5 significant digits. This is one of the easiest aspects of the math portion of the exam, and I am very nervous about getting hung up on a similar question during my exam.

Any input on this would be greatly appreciated.

I'm not an ASQ official, but I agree with your position that the advertised answer is incorrect.

Hopefully you will get an apology from ASQ and they will correct it in a future edition. Please don't get hung up or distracted by the author's error and the ASQ's Help Desk's response. Focus on the big picture. Learn all you can.

I have taken several ASQ exams (CQE and CQM/OE) after having spent around 20 hours studying the ASQ Body of Knowledge each time, and have passed each exam. Unfortunately they don't show you which exam questions you got wrong and why, so that isn't a learning opportunity.

Best wishes on your exam,

John

Hey Jesse,

In my experience, I have found that it is not uncommon at all to encounter minor errors in the ASQ material such as this, and I would like to encourage you that you are taking the right approach by paying close attention to the semantics of the question. That, alone, is one of the best tools you can bring with you into an ASQ exam! Based exclusively on the semantics of the question, your selection for “truncation” to “significant digits” is correct. (If they had alternatively asked for something like the most accurate rounded answer with significant digits, then it should have been b; or likewise as you mentioned, if they asked for “decimal places” instead of “significant digits,” etc.) I would like to hope that these types of errors do not exist on the exams, but they definitely do exist in the training and preparation content. Be assured that you are understanding correctly and be prepared to note occasional discrepancies.

I agree with you. Option c has 4 significant figures. I'm not sure how to get this fixed; the Learning Team clearly needs to correct the answer key and/or the terminology.

Here's a web reference for you:

How do you round to three significant digits?

Rounding to 3 significant figures is probably the most common way of rounding off. Rounding the number off to 3 significant fugures means you require

**3 non-zero digits from the start of the number**. So in example 1, 27.1258 gets rounded to 27.1. In example 2, 3.12845 gets rounded to 3.13.

In mathematics,

**truncation**is limiting the number of digits right of the decimal point. Truncation - Wikipedia

Reference: The CQI Handbook (3rd edition), page 11: TRUNCATING is to display a result with a certain number of decimal places, we can choose to truncate the number. For example, we can truncate the number 3.527 to two decimal places by writing 3.52

Good luck on your exam.

Jim

Mr. West,

I think to answer your question, there are two thinks you should know well they are TRUNCATE and N SIGNIFICANT DIGITS (where N is a whole number). Let me explain with my little knowledge. Truncate is different than Rounding (more explanation can be found in the dictionary or in the CQT BOK. I believe N significant digits means N numbers after the decimal point and not N total numbers. I think using these two definitions, the answer is clearly A.) 7.4688.

Example if the number to be truncated was 7589314.4688527 then the answer would be: 7589314.4688.

Hope this clarifies the confusion.

Thanks

Jim, you are correct about truncation, but this Wikipedia definition doesn't talk about significant digits, it talks about the number of digits to the right of the decimal point. The exam question clearly states the number of significant digits, so I would still guess that b) is the correct answer.

I totally agree with, Ms. Sarah, and, Mr. Andre! It appears the question should have read (or implied) as “truncated to four ‘decimal’ places”.

I have been watching this thread with some amusement. I thought I would share my two cents.

From CQT BOK: IV.B.4: Rounding rules Use truncation __and__ rounding rules on both positive and negative numbers. (Apply)

Thoughts:

- Truncation and rounding are part of the same knowledge statement/requirement.
- The title of the knowledge statement is Rounding Rules.
- The item is set as Apply, which is a mid-level on the Bloom’s Taxonomy (Apply: Know when and how to use ideas, procedures, methods, formulas, principles, theories, etc.)
- How many of us in Industry says: “Don’t round but do truncate to 3 significant digits?”

This is a bit of a “got you” question that does not test real-world knowledge from my point-of-view. At the end of the day does knowing how to answer this question make some a better CQT. I really don't think so personally.

Hi everyone ! I think the question is not correct.

It should say something like: “Truncate the following number 7.4688523 to 4 significant digits.”

Then you have a basis for the answer.

Then you can drive an answer.

The answer would be 7.4688

Another example:

Truncate the following number 7.04688523 to 4 significant digits.

The answer would be 7.04688

Zero's after the decimal don't count when counting significant digits.

ie. 0.0001 has 1 significant digit.

Rounding is different when combined with truncating. Most large organizations have an SOP on Rounding and truncating for significant digits. Analytical instrumentation has a profound impact on the same subject. Hope this helps in the discussion.

-Regards - Bill F.

Another example:

Truncate the following number 7.04688523 to 4 significant digits.

The answer would be 7.04688

Zero's after the decimal don't count when counting significant digits.

ie. 0.0001 has 1 significant digit.

Can you cite me a source for this? I did not realize there was such a variety of understandings and now my head is fairly spinning.

Taking exams in general, especially some of the ASQ certification ones, there seems to be at least one that is in the gray area or incorrect. Don't worry too much about that one, for the most part the exam is correct. Keep up the good work and good luck on the exam.

Agree Ken. I've never heard that a zero in the middle of a number is not a significant digit.

Now if the number had only zeros on the left like 0.04688 that is a different story.

Please have references for your opinions!

**What is a significant number? and 'Trapped zeros"?**

“Zeros appearing between two non-zero digits (trapped zeros) are significant. Example: 101.12 has five significant figures: 1, 0, 1, 1, and 2.”

“All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4, and 5).” So number before the decimal point count towards the sig fig counting.

**Truncation vs rounding: **

You are correct. Truncating is chopping off the numbers leaving only four without significantly changing the value of original number