Handy approximations

**mklotz** · Oct 29, 2020, 12:17 PM

It's always handy to be able to do rough calculations mentally to check the work of yourself and others. If you live in the measurement system backwater of the USA, mental conversions between metric and inferial are frequently needed. Below I've collected some approximations that make the arithmetic much simpler and thus easier to do mentally.

PI

22/7 was ok for grade school but far more accurate is 355/113. A good mnemonic is write down the first three odd integers twice, i.e. 113355. Now put a slash in the middle - 113/355 and reverse the numbers - 355/113. Handy for calculators that don't have a pi key.

METERS TO FEET

A meter is about 3.3 feet. Mentally, multiplying by 3.3 is easy; multiply by 3 then add a tenth of the result. 5 meter * 3.3 = 15 + 1.5 =16.5 feet. (Correct value = 16.4...)

KILOMETERS <=> MILES
A kilometer is about 0.6 miles (Correct = 0.621...) A mile is about 1.6 kilometers (Correct = 1.609...)

KILOGRAMS TO POUNDS

A kilo is about 2.2 pounds. Again, multiplying by 2.2 is easy; 5 kilo * 2.2 = 10 + 1 = 11 lb (Correct = 11.02...)

A metric tonne (note spelling) is 1000 kg so about 2200 lbs or very close to the inferial long ton.

CENTIMETERS TO INCHES

A centimeter is about 0.4 inches. 30 cm * 0.4 = 12 inches (Correct = 11.81...)

MILLIMETERS TO INCHES

A millimeter is about 0.04 inches. Multiply by 4 and move decimal to left two places. 150 mm * 0.04 = 600/100 = 6 inches (Correct = 5.906...)

FRACTIONAL INCHES <=> MILLIMETERS

Keep doubling numerator and denominator until the denominator is 256. Then the numerator divided by ten is the equivalent in mm with an error of only 0.78%. 13/64 = 26/128 = 52/256 -> 52/10 -> 5.2 mm (correct value = 5.159375 mm)

For millimeters to inches, multiply mm by 10 and divide by 256, keep dividing numerator and denominator by 2 until done.
6 mm => 60/256 = 30/128 = 15/64 (error = 0.78%)

SPEED OF LIGHT

3*10^8 meters/sec is about 1 foot per nanosecond (Correct = 0.984... ft/nanosec)

SUBTENDED ANGLE

One minute of arc at a distance of 100 yards subtends about 1 inch.

(1/60 deg) * (pi/180 rad/deg) * (3600 inches) = pi/3 inches = 1.047 inches

Thus one arcsecond (1/60 of an arcminute) would subtend 1.047/60 = 0.0175 inches

CUBIC FOOT OF WATER TO POUNDS AND PRESSURE AT DEPTH

A cubic foot of water weighs about 62.4 lbs. So, for each foot below the surface, the pressure increases by 62.4 / 144 = 0.433 psi

A one foot head of water exerts a pressure of 0.433 psi. A 2.31 feet head of water exerts a pressure of one psi.

A cubic meter of water contains 1000 liter and a liter of water weighs a kilogram so a cubic meter of water weighs a metric tonne.

FIFTHS

A gallon is 3785 milliliters so a fifth of that is 757 ml which explains why your "fifth" of whiskey is 750 ml. A quart is 946 ml so your "fifth" is 750/946 = 0.793 qt. Call it 0.8 and you're close enough.

**Carnel** · Oct 30, 2020, 03:27 AM

Hi Marv, I saw you where writing "metric and inferial". Was this intentional or a Freudian slip of the keyboard?

**mklotz** · Oct 30, 2020, 09:37 AM

Originally Posted by Carnel

Hi Marv, I saw you where writing "metric and inferial". Was this intentional or a Freudian slip of the keyboard?

I live in the USA, the only industrial nation on earth that doesn't use the metric system. Usonians will tell you that we use the Imperial system but that isn't strictly true. True, we obtained most of our system from Britain but we further botched and confused it into the mess now known as "American Customary Units". That's a mouthful to say or write and few will know what you're talking about.

I decided to make up my own designation for a system that has seven different units all called "barrel". My "inferial" is a portmanteau of "inferior/infuriating" and "Imperial".