4 ms·

Slightly more accurate .. 1: 0.0 2: 0.3 3: 0.475 4: 0.6 (22) 5: 0.7 6: 0.775 (23) 7: 0.85 8: 0.9 (222) 9: 0.95 (3*3) T

Slightly more accurate .. 1: 0.0 2: 0.3 3: 0.475 4: 0.6 (2*2) 5: 0.7 6: 0.775 (2*3) 7: 0.85 8: 0.9 (2*2*2) 9: 0.95 (3*3) The biggest error is 7 at +0.577% ... 0.845 is almost perfect. The others are maximum +0.45% off. So you only need to remember: 2: 0.3 7: 0.85 9: 0.95 1.4 = sqrt(2) -> 0.15 3 = sqrt(9) -> 0.95/2 = 0.475 pi = ~sqrt(10) -> 0.5 4 = 2*2 -> 0.6 5 = 10/2 -> 0.7 6 = 2*3 2pi = 2*sqrt(10) -> 0.3+0.5 = 0.8 8 = 2*2*2 -> 0.9

madcaptenor 1y ago
You barely even have to remember 9: 0.95 since you can get it by interpolation between 8 and 10.
- brucehoult 1y ago
  Yup. Put the effort into remembering a 3 digit log for 7 instead? Or keep the same precision with ... 7 = ~sqrt(100/2) -> (2-0.3)/2 = 1.7/2 = 0.85 Log 2 is all you need? Or even ... 7 = sqrt(sqrt(2401)) = (3*8*100)^(1/4) -> 0.95/8 + 0.3*3/4 + 2/4 = 0.12 + 0.225 + 0.5 = 0.845 VERY accurate, but that's getting to be too much.
arkeros 1y ago
You also don't need to remember 7, as 2*7^2 =~ 100 => log 7 =~ (2 - 0.3) / 2 = 0.85
- brucehoult 1y ago
  Yes, as I mentioned in one of my other replies. Or 2400^0.25. Same for 9: sqrt(81) = sqrt(8 * 10) -> (0.3*3 + 1) / 2 = 0.95 At some point it's easier to remember a few numbers than calculate a lot of formulas.
adrian_b 1y ago
I find much more useful to memorize the inverse of that table, i.e. the decibel table. The numbers corresponding approximately to 0 dB, 1 dB, 2 dB, 3 dB etc. (1.0, 1.25, 1.6, 2.0 etc.; more accurate values, like 1.26 or 1.58 instead of 1.25 and 1.6 are typically not needed) are also frequently encountered as such in engineering practice as belonging to various series of standard nominal values, which makes them more useful to have in mind. Then for any mental computation, it is trivial to convert mentally a given number to the corresponding dB value, perform the computation with additions and subtractions instead of multiplications and divisions, then convert back the dB value to the linear number corresponding to the result. Doing mental computations in this way, even if it has only about 2 correct digits at most, is enough for debugging various hardware problems, or even for catching software bugs, where frequently an impressive numbers of significant digits is displayed, but the order of magnitude can be completely wrong.
- madcaptenor 1y ago
  Since 3 dB is so nearly 2.0, you can derive that series by taking small powers of two, say from 2^(-4) to 2^5 or 2^6: 0.0625, 0.125, 0.25, 0.5, 1, 2, 4, 8, 16, 32, (64) and then multiplying everything by factors of 10 to get it between 0 and 10: 1, 1.25, 1.6, 2, 2.5, 3.2, 4, 5, 6.25 (or 6.4), 8
  - adrian_b 1y ago
    You are right, so this is how the series of standardized nominal values that has been traditionally used for some quantities, like maximum dissipated powers for resistors, maximum operating voltages for capacitors, maximum powers for motors, hexagonal nut sizes for some ancient packages for stud-mounted power semiconductor devices, etc., has been obtained. Apparently whoever have standardized first this series of values have not been able to make their mind to choose between 6.25 and 6.4, therefore 6.3 has been chosen instead of any of those 2 values.

Slightly more accurate .. 1: 0.0 2: 0.3 3: 0.475 4: 0.6 (2*2) 5: 0.7 6: 0.775 (2*3) 7: 0.85 8: 0.9 (2*2*2) 9: 0.95 (3*3) T

madcaptenor 1y ago

You barely even have to remember 9: 0.95 since you can get it by interpolation between 8 and 10.

brucehoult 1y ago
Yup. Put the effort into remembering a 3 digit log for 7 instead? Or keep the same precision with ... 7 = ~sqrt(100/2) -> (2-0.3)/2 = 1.7/2 = 0.85 Log 2 is all you need? Or even ... 7 = sqrt(sqrt(2401)) = (3*8*100)^(1/4) -> 0.95/8 + 0.3*3/4 + 2/4 = 0.12 + 0.225 + 0.5 = 0.845 VERY accurate, but that's getting to be too much.

arkeros 1y ago

You also don't need to remember 7, as 2*7^2 =~ 100 => log 7 =~ (2 - 0.3) / 2 = 0.85

brucehoult 1y ago
Yes, as I mentioned in one of my other replies. Or 2400^0.25. Same for 9: sqrt(81) = sqrt(8 * 10) -> (0.3*3 + 1) / 2 = 0.95 At some point it's easier to remember a few numbers than calculate a lot of formulas.

adrian_b 1y ago

I find much more useful to memorize the inverse of that table, i.e. the decibel table. The numbers corresponding approximately to 0 dB, 1 dB, 2 dB, 3 dB etc. (1.0, 1.25, 1.6, 2.0 etc.; more accurate values, like 1.26 or 1.58 instead of 1.25 and 1.6 are typically not needed) are also frequently encountered as such in engineering practice as belonging to various series of standard nominal values, which makes them more useful to have in mind. Then for any mental computation, it is trivial to convert mentally a given number to the corresponding dB value, perform the computation with additions and subtractions instead of multiplications and divisions, then convert back the dB value to the linear number corresponding to the result. Doing mental computations in this way, even if it has only about 2 correct digits at most, is enough for debugging various hardware problems, or even for catching software bugs, where frequently an impressive numbers of significant digits is displayed, but the order of magnitude can be completely wrong.

madcaptenor 1y ago
Since 3 dB is so nearly 2.0, you can derive that series by taking small powers of two, say from 2^(-4) to 2^5 or 2^6: 0.0625, 0.125, 0.25, 0.5, 1, 2, 4, 8, 16, 32, (64) and then multiplying everything by factors of 10 to get it between 0 and 10: 1, 1.25, 1.6, 2, 2.5, 3.2, 4, 5, 6.25 (or 6.4), 8
- adrian_b 1y ago
  You are right, so this is how the series of standardized nominal values that has been traditionally used for some quantities, like maximum dissipated powers for resistors, maximum operating voltages for capacitors, maximum powers for motors, hexagonal nut sizes for some ancient packages for stud-mounted power semiconductor devices, etc., has been obtained. Apparently whoever have standardized first this series of values have not been able to make their mind to choose between 6.25 and 6.4, therefore 6.3 has been chosen instead of any of those 2 values.