The Rule of 3 Significant Digits

Two people have shaped how I guess an answer.

Their comments and guidance have tailored how to form a quick estimate, my ability to articulate a hunch and the effectiveness of those guesses.

You probably guess or make a rough estimate regularly. How good is your gut feel? Do you keep track and score yourself?

Making an estimate should be second nature for you. It’s not something to do in public, too often. The practice can aid you in numerous ways.

Physics, Calculations, and Estimates

In my first physics class in college, we regularly ‘enjoyed’ pop quizzes. One, in particular, provided a lesson that has stuck with me for my entire life.

Here is the quiz question (as far as I recall it’s wording)

“How many piano tuners are there in New York City? 3 minutes, show your work.”

The homework for the class from the previous class included calculating acceleration given force on mass or something like that. Not a hint that we would be tested on census values.

There were a few groans across the room. A few pencils started to scratch out some answer.

How would you answer? What work would you show? Keep in mind I went to college a long time ago, and we did not enjoy the benefits of a Google search or anything even remotely similar. I had not lived in NYC nor played piano.

Give yourself three minutes, do not use the internet (if you haven’t already), and add you answer to the comments section below. Show your work.

The lecture after the quiz discussed the value of making a reasonable estimate or educated guess before performing the experiment or calculation. Physics involves math and just knowing the formulas does not guarantee you will get the right answer.

He likely mentioned a quote, or I ran across it later, by John Archibald Wheeler attributed to his book, Spacetime Physics.

Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun! – John Archibald Wheeler, Spacetime Physics

This process helped me throughout my career. More than once helping me catch a missing sign that altered a calculated result. When I would guess the result of a calculation should show an increasing speed, and my calculation shows the falling rock has a decreasing speed over time, I would find the dropped negative sign and correct my calculation.

Another exercise we did in class was to sum a set of numbers, quickly. The first step was to jot down a guess, an order of magnitude or rough estimate. If the list is ten positive three-digit numbers, the result is going to be greater than 1,000. How much more, roughly? If the results of you addition work is -237, could that possibly be right?

Having the estimate allows you to compare your answer to your hunch. It provides a check step for your calculation.

Just because Excel churns out a number doesn’t mean it’s right. How do you know or at least how do you check?

Improve the Effectiveness of Your “Back of the Envelope” Estimates

I’d been making these educated guesses regularly for years. Then I shared an estimated value of a proposed project with Helen.

Helen had the office next to mine at HP at the time. She is an inventive and wicked smart engineer. I often shared ideas and proposals with her as her insights and advice always improved my work.

The proposal was exciting for me as I expected $10 million in value for a rather modest investment of time.

She stopped me right there. She said, “$10 million, really? I don’t believe that.” Or something to the effect.

Continuing the discussion, I quickly went over the assumptions and back of the envelope calculations that supported the claim.

She didn’t question the logic nor the actual results. Rather she wondered if the nice round numbers I used could be slightly altered. Sure, they only rough estimates, such as 100,000 customers or $1,000 in the cost of each failure, etc.

She said when she hears a nice round number she instantly knows it is a guess or estimate. Her guard goes up as she becomes distracted by the round number rather than focusing on the logic and assumptions.

Helen recommended I alter the final result to include three significant digits. Instead of $10 million, how about $9.87 million. It’s about the same as the result I got using a sequence of round numbers, yet Helen suggested it was “a bit more believable.”

Hum. Never thought of that. I always focused on the assumptions and logic, not the result. I thought the order of magnitude was sufficient to convey the result.

As you know, everyone filters what they hear and accept. Recognizing some recoil when they hear a nice round number meant I could lessen the effects of that kind of filter by simply using a three digit estimate.

So, I tried it. Over the next year each time I presented a guest or estimate I alternated between nice round numbers and estimates with three significant digits.

The round number estimates always generated questions about the values and numbers that went into the result. The three significant digit estimate often were not questioned or enjoy questions about the assumptions and logic only. I kept track that year and twice as many proposals using the three significant digit rule moved forward.

You will have to make quick estimates, work out a rough return on investment, or forecast return on investment values. In these cases you need to make a guess, then using the set of assumptions and a bit logic refine your estimate in just a short time (never having all the data you need). When presenting the results try using three significant digits.

Record these estimates and remind yourself to check how well it turns out if possible. Also, note how your audience responds to the ‘believable’ estimate you present.

Your Next Estimate

How many will view, share, and respond to this article?

Please, right now, without too much thought, add your guesses to the comment section below.

A month after this article posts I’ll tally up the shares and post the actual answer. I think I can find counts for views and the comment count will suffice for the last element.