Re: Deane Kidd and the Metric System


Ian Newman <ian_new@...>
 

Hi,
On the topic of conversion between Imperial and SI units of length there is a well known method of quickly converting aliquot parts of an inch to millimetres using the approximation 254 = 256

If you have a fractional inch dimension, multiply top and bottom of the fraction by two repeatedly until the denominator equals 256.  Shift the decimal point of top and bottom one place to the left.  The numerator now equals the inch dimension times 25.6, which is the equivalent number of millimetres (to less than 1% error)

For example, take a fractional inch dimension - 3/8

3/8 = 6/16
3/8 = 12/32
3/8 = 24/64
3/8 = 48/128
3/8 = 96/256

3/8 inch = 9.6mm (to better than 1%)
Actual conversion = 9.525mm

In actual use, simply count how many times you need to multiply the denominator to get 256, then multiply the numerator by two that many times and write down the answer, slipping in the decimal point as you do so.

E.g. 9/16
Multiply the denominator by 2 four times (32, 64, 128, 256).  Now multiply the numerator by 2 four times - 18, 36, 72, 144 - giving 14.4mm (actual value 14.29 to four sig. fig.)

If you have whole numbers of inches, convert to irrational fractions first:
2 3/4 inch = ((2 x 4) +3)/4 inch
=11/4 inch
= 704/256
= 70.4mm (actual value 69.85)


You can improve the accuracy (using mental arithmetic) by reducing the value of the answer by 1%. Take the first significant digit of the result, move the point two places left (divide by 100) and subtract from the original result.

Doing this to the examples above gives:

3/8 inch = 9.6mm
Better approximation:
3/8 = 9.6 - 0.09
= 9.51mm
Actual value = 9.525mm

9/16 inch = 14.4mm
Better approximation:
9/16 = 14.4 - 0.1
= 14.3mm
Actual value = 14.29mm

2 3/4 inch = 70.4mm
Better approximation:
2 3/4 = 70.4 - 0.7
= 69.7mm
Actual value = 69.85mm

Even I can multiply by two in my head......

All the best,
Ian




From: "Barry n4buq@knology.net [TekScopes]" <TekScopes@yahoogroups.com>
To: TekScopes@yahoogroups.com
Sent: Thursday, 14 December 2017, 13:47
Subject: Re: [TekScopes] Deane Kidd and the Metric System

  Instead of a ruler for size comparison, perhaps Walter can post pictures of those knobs alongside an assortment of coins from all around the world? :)

Thanks,
Barry - N4BUQ
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