I have been reading the posts on significant figures and wonder why a quality organization would put such a question on an exam about significant figures to the left of the decimal. Without additional context, it could lead down a false path of assumptions. If I am dealing with a set of numbers like, 15,000, 20, 000, 10,000, and 35,000 then maybe there is some context that there are significant figures to the left. If my set of number is like 14,998, 14,999, 15,000, 15,002, and 15,005 then the zeroes in 15,000 are just as significant as an other digit. A zero is a value so to state it is not significant without context does not seem valuable. The only value I see is that we may be able to change the units to thousands instead.

There could be another related topic about accuracy and precision for a measurement system where the process itself cannot repeat a same value to a certain set of digits, but this context also was not mentioned (e.g. 15,000, 15,002, 14,995, and 15,049 would all be stated as 15,000 because a measurement system is only accurate to the 1,000 units).

It has been an interesting discussion but it makes me wonder if some of the questions focus on items of little importance compared to the more critical areas of knowledge for a quality professional. So, while I have no assistance to provide help with the original question, I have enjoyed reading the responses.

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Ronald Post

Quality Manager

Westinghouse Electric Company

Shanghai China

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Original Message:

Sent: 03-12-2018 21:21

From: Claire Everett

Subject: Significant Digits

Hi David

I found a better resource for you about significant figures https://chem.libretexts.org/Core/Analytical_Chemistry/Quantifying_Nature/Significant_Digits if goes through separate rules for numbers with and without decimal places.

The section on rounding significant digits and example 1.7 seems to be particularly relevant to your question.

Based on this however I have to agree with you on your answer to the 100cm cubed question, 100 has only 1 significant figure.

Best wishes

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Claire Everett

Prosegur Australia

St Leonards

(61)294909926

Original Message:

Sent: 03-10-2018 23:42

From: David MacLeod

Subject: Significant Digits

Thank you Claire - good idea to take a look at the Wikipedia entry on significant digits!

Thank you William - yes, I also have the ASQ Certified Quality Technician Handbook, and Gary Griffith's Quality Technician Handbook. Neither of those discuss significant digits. Perhaps not likely to come up on the cert exam.

Thank you Joe. According to the QCI Primer, "A good quick rule of thumb...is to identify the incoming data with the fewest significant figures and to report exactly one more figure in the final answer." Therefore, in your example, the answer would be 7.11?

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David MacLeod

Certified Quality Associate

Samson Rope Technologies, Inc.

Ferndale WA

(360)325-7884

Original Message:

Sent: 03-07-2018 10:28

From: Joe Wojniak

Subject: Significant Digits

Hi- this probably won't help with an exam question, but I try to think of significant digits in terms of the precision of the gage that I'm using. For example- calipers will read-out to 4 decimal places 0.0000. However, the fourth decimal place is usually 0 or 5: 0.0005 or 0.0000. And I've also read that measurements taken with calipers are typically reproducible to .001". For recording purposes, I record the measurement exactly as displayed on the calipers. However, when taking the average (a.k.a. mean or Xbar) I'll round to 3 decimal places (0.000).

The purpose of significant digits is to ensure that the calculated result (in this example the mean) isn't being reported as being more precise than the measurements themselves.

The unit conversion problem is also a typical situation. 1" = 2.54 cm

So, if I have 2.8" and convert to metric: 2.8" * 2.54 cm = 7.112 cm

I would round to 7.1 cm because the measurement has 2 significant digits (2.8") and 2.54 cm is a conversion factor. I think what I'm doing is using the least precise number (the measured value) to determine the number of significant digits (2 instead of the 3 in the conversion factor).

I've found this to be a practical method, but it may not agree with the "correct" exam answer!

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Joe Wojniak

Sr. Quality Engineer

Longmont CO

Original Message:

Sent: 03-06-2018 15:12

From: William LaFollette

Subject: Significant Digits

David

While there may be significant numbers questions on the actual exam, I would caution on using the QCI primers as a sole reference.

While I often use that material it is not on the recommended references listing for the exam.

The questions on the exam are derived from those references listed on the ASQ site. If you are needing a rationale or clarification on a discrepancy in the QCI materials I would advise you contact them directly.

Look at the practice exams on the ASQ site as well.

Best,

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Dr. William 'Will' LaFollette

Original Message:

Sent: 03-04-2018 19:18

From: David MacLeod

Subject: Significant Digits

I'm studying for the CQT exam. According to the QCI Primer (7th edition, chapter 9, page 15), the number 2500 has just two significant digits - "no printed decimal point, count nonzero digits only."

On the next page of the Primer it describes how to calculate with significant digits: "A good quick rule of thumb...is to identify the incoming data with the fewest significant figures and to report exactly one more figure in the final answer."

So, if I take 2500 inches, and calculate a conversion to feet, I divide by 12, I get the result 208.33333. Then for my final answer, I report 3 significant digits: 208 feet. Is this correct?

Next, I take the CQI practice exam on the CD-ROM that is presumably based on the Primer referenced above, and come across the following question:

A volume containing 100 cubic centimeters would convert to how many cubic inches?

A) 6 cubic inches

B) 6.1 cubic inches

C) 6.10 cubic inches

D) 6.102 cubic inches

My answer, attempting to follow the instructions of the Primer, is to say 100 cubic centimeters has only 1 significant digit (counting nonzero digits only). Therefore, the answer should have 2 significant digits. So I choose answer B: 6.1 cubic inches.

However, this answer is marked as incorrect, and I am told: "Since the fewest incoming significant digit is three, four figures should be reported in the answer. Answer D is correct.

Am I missing something, or is there a contradiction between the Primer and the CD-ROM? I can't find an explanation of this in my other two books (ASQ Certified Quality Technician Handbook, or G. Griffith's The Quality Technician's Handbook - 4th edition).

I would like to know how to correctly answer this question if something like it comes up on the actual CQT exam.

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David MacLeod

Certified Quality Associate

Samson Rope Technologies, Inc.

Ferndale WA

(360)325-7884

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