Why Whittling Down Precision Could be Your Best Finishing Touch (Chris Mangelsdorf)

Really well done.. https://www.youtube.com/watch?v=pdVfni3gADo

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Significant Digits: Don'ts and Do's

Don't use too many digits

Too many digits imply fake precision.

Quoting a shoe size as 10.314 inches when shoes only come in half sizes. Presenting a Spurious Free Dynamic Range (SFDR) of 97.822 dB and implying that the last digits (.822) are meaningful when they represent a tiny, likely insignificant difference in amplitude (0.2% for rounding to 97.8).

Don't include digits that are merely noise

Variability across trials shows those digits aren't meaningful.

Taking two measurements of the SFDR. If the first measurement is 97.822 dB and the second is 97.835 dB, the digits after the first decimal place are changing and are likely noise.

Don't include digits that are context-dependent

Results that vary with setup shouldn't be reported precisely.

Measuring a distortion component where results vary significantly depending on minor condition changes, such as reversing a Balun which caused a 10 dB difference. Reporting a precise value with multiple decimal places for a single measurement when the number is highly dependent on external factors is misleading.

Don't include digits irrelevant to the application

Too much detail distracts from what matters.

Customers often think in terms of round numbers for parameters like gain (~10 dB) or noise figure (28 dB). Providing a gain value like 9.952 dB might be irrelevant if the application only needs the value to the nearest whole number or first decimal place. The precision might be limited by other system components, like connectors limiting ADC accuracy.

Don't blindly trust simulator precision

Simulators output clean numbers, but real devices aren’t that exact.

A simulator outputting a value like 7.12 x 10^-4 for a component. While mathematically precise in the simulation, this doesn't mean a physical component can be controlled or measured to that degree of accuracy.

Do ensure only the last digit is uncertain

Only the last digit should carry estimation.

Measuring the length of a Twinkie. If you are certain it's 9.9 cm but estimate the next digit to be 4, you write 9.94 cm. The '9' and first '.9' are certain, while the last '4' is the estimate or uncertain digit.

Do use sig digits to imply precision

Readers infer precision from how many digits you use.

The number 123,000 written without a decimal point typically implies three significant digits (1, 2, 3). Writing 123,000.0 implies six significant digits, indicating precision down to the tenths place. This notation signals intent about accuracy.

Do match calculation precision to inputs

Never claim more precision than your inputs had.

If you multiply 1.23 (three significant digits) by Pi (which has infinite significant digits), your result should only have three significant digits (e.g., 1.23 * 3.14159... rounds to 3.86). Another example is multiplying a number with five significant digits by a number with three significant digits; the result should be rounded to three significant digits.

Do use scientific/engineering notation

It clarifies scale and sig digits clearly.

Writing 123,000 volts as 123 kilovolts clearly shows three significant digits. Writing 0.0123 volts as 12.3 millivolts also shows three significant digits (the leading zeros are not significant). To show four significant digits for 123,000, you might write it as 123.0 kilovolts.

Do limit to 3 sig digits unless justified

More than 3 digits usually adds noise, not clarity.

If you have a number like 8.11 x 10^-9 for the probability of metastability or a component tolerance of ±20%, consider whether presenting four digits (8.11) is truly justified, or if 8.1 x 10^-9 is a more realistic representation of the known accuracy.

Do ask: Accuracy? Context? Usage?

Use only as much precision as is truly needed.

Before stating an SFDR of 97.822 dB, ask: Is my measurement setup accurate enough to distinguish between 97.82 dB and 97.83 dB? Would the result change if I used a different cable? Does the customer designing a receiver need to know the SFDR to the hundredth of a dB?