Here is the first article on your math lessons: IN AND OUT OF THE METRIC SYSTEM (FROM ALTERNATIVE APPROACH TO MATHEMATICS VOL. I) By: Diosdado F. Fragata There are two common systems of measurement; the British System (in-lbs- sec), and the Metric System (cm-gm-sec). Conversion of units in the British System uses numerous factors without a common relationship while that in the Metric System uses decimal factors (multiples of 10, 100, 1000 etc). Obviously, the Metric System is simpler than the British System. In view of this, some countries that used to employ the British System, including its origin, Great Britain, have chosen to go Metric. The United States however did not shift to metric. This is probably because changing the system of measurement of a big industrialized country would entail a very high retooling cost. Developing countries are the most affected by this shift to the metric system because of several factors like: a. They cannot afford the high cost of retooling. b. They cannot be selective with materials on the basis of system of measurement as they still rely on imports. The choice is therefore a matter of price and not of measure system. The Philippines is a classic example. The law requires that the measure used in trade and industry should be in metric. Construction plans are required to be in metric measures, but most available materials are in the British System such as lumber, nails, hollow blocks, plywood etc. The end user is therefore left to figure out for himself if the available materials in the market meet the specifications or if the specifications should be changed to fit the available materials. Thus instead of contending with only the conversion of units in a single system of measurement, the consumer is also faced with the task of conversion of units from one system to the other, a task which to most people is a mathematical nightmare. The following procedures are intended to provide alternatives to the usual methods of conversion: a. CONVERSION OF INCHES TO CENTIMETERS 1 inch is equivalent to 2.54 centimeters.For practical purposes 2.5 may be used since .04 is a very small quantity and will result to only about 1.6% error if disregarded. Then the conversion can be done as follows: Step1. Move the decimal point of the given length one place to the right and divide the result by 2. Step2. Divide the result of Step 1 by 2 to get the equivalent of the given length in centimeters. Example: Convert 16 inches to centimeters Solution: Step 1. 160/2 = 80 Step 2. 80/2 = 40 cm The actual value of 16 inches in centimeters is 40.64. The error of 0.64 is only 1.57% of the true value. b. CONVERSION OF CENTIMETERS TO INCHES This is basically the reverse of the previous operation and is performed as follows; Step1. Move the decimal point of the given length one place to the left then multiply the result by 2. Step2. Multiply the result of step 1 by 2 to get the value of the given length in inches. Example: Convert 50 cm to inches Solution: Step 1. 5 x 2 = 10 Step 2. 10 x 2 = 20 inches The actual value of 50 cm in inches is 19.685. There is an error of 0.315, which is only 1.6 % of the true value. c. CONVERSION OF KILOGRAMS TO POUNDS 1 kilogram is equivalent to 2.205 pounds. For practical purposes, 2.2 will suffice to provide a high degree of accuracy. The conversion can therefore be done as follows; Step1. Multiply the given weight by2. Step2. Move the decimal point of the result of Step 1 one place to the left. Add this new number to the result of Step 1 to get the value of the given weight in pounds. Example: Convert 12 kilograms to pounds Solution: Step 1. 12 x 2 = 24 Step 2. 2.4 + 24 = 26.4 pounds The actual value of 12 kilograms is 26.46 pounds. The error of 0.06 is only 0.227% of the true value. d. CONVERSION OF POUNDS TO KILOGRAMS Instead of dividing the given weight in pounds by 2.2 to convert it to kilograms, the conversion may be done as follows; Step1. Move the decimal place of the given weight one place to the left then subtract the result from the given weight. Step2. Move the decimal place of the given weight two places to the left and add the result to that of Step 1. Step3. Divide the result of Step 2 by 2. The result of this Step is the value of the given weight in kilograms. Example: Convert 150 pounds to kilograms Solution: Step 1. 150 -15 = 135 Step 2. 1.5 + 135 = 136.5 Step 3. 136.5 / 2 = 68.25 kg 150 pounds is 68.027 kilograms, accurate to 3 decimal places. The error of 0.223 kilograms is only 0.33% of 68.027. e. CONVERSION OF STATUTE MILES TO KILOMETERS 1 statute mile is 1.6098 kilometers. When rounded to 1.61 kilometers, the conversion from statute mile to kilometers can be done as follows; Step 1. Divide the given distance by 2 and add the result to the given number. Step 2. Move the decimal point of the given number one place to the left. Add the result to that of Step 1. Step 3. Move the decimal place of the given number two places to the left and add the result to that of Step 2. The result of this Step is the value of the given distance in kilometers. Example: Convert 60 miles to kilometers Solution: Step 1. 60 /2 + 60 = 90 Step 2. 6 + 90 = 96 Step 3. 0.6 + 96 = 96.6 km 60 miles is equivalent to 96.585 kilometers. The error incurred in the above procedure is only 0.015 which is just 0.016% of the exact value. f. CONVERSION OF KILOMETERS TO MILES In convert kilometers to miles the given distance is usually divided by 1.6098, but dividing a number by a five-digit divisor is extremely difficult. The process however is simplified by the following procedure; Step 1. Divide the given number by 2. Step 2. Move the decimal place of the given number one place to the left and add the result to that of Step 1. Step 3. Move the decimal place of the given number two places to the left then multiply the result by 2. Add the product to the result of Step 2. Step 4. Move the decimal place of the given number 3 places to the left and add the result to that of Step 3. The result of this step is the value of the given distance in miles. Example: Convert 120 kilometers to miles Solution: Step 1. 120 /2 = 60 Step 2. 12 + 60 = 72 Step 3. 1.2 x 2 + 72 = 74.4 Step 4. 0.12 + 74.4 = 74.52 miles 120 kilometers is 74.545 miles accurate to 3 decimal places. The error incurred by the procedure is negligible. g. CONVERSION OF DEGREES FAHRENHEIT TO DEGREES CENTIGRADE The formula for converting degrees Fahrenheit to Centigrade is as follows: C= (5/9) x (F – 32) The conversion however can be approximated by the following operation; Step 1. Subtract 32 from the given number. Step 2. Divide the result of step 1 by 2. Step 3. Make a tabular ladder starting with the result of Step 2 but move the decimal place of the number one step to the left for each entry. Make at least five entries. Step 4. Sum up the entries. The result is the value of the given temperature in degrees centigrade. Example: Convert 200 degrees Fahrenheit to degrees Centigrade Solution: Step 1. 200-32 = 168 Step 2. 168/2 = 84 Step 3. 84.0 8.40 0.840 0.0840 0.00840 Step 4. 93.33240 degrees C Note that if we keep on adding entries to the ladder the sum would approach 93.33333…degrees C, which is the true value of 200 degrees F. h. CONVERSION OF DEGREES CENTIGRADE TO DEGREES FAHRENHEIT The formula for converting degrees Centigrade to degrees Fahrenheit is: F = (9/5) x C + 32 The calculation can be done as follows; Step 1. Multiply the given number by 2 Step 2. Move the decimal point of the result of Step 1 one place to the left and subtract the result from that of Step1. Step 3. Add 32 to the result of Step 2. The result of this step is the value of the given number in degrees Fahrenheit. Example: Convert 100 degrees Centigrade to degrees Fahrenheit Solution: Step 1. 100 x 2 = 200 Step 2. 200 – 20 = 180 Step 3. 180 + 32 = 212o Fahrenheit The result obtained by this procedure is the exact equivalent of temperature in degrees Centigrade to degrees Fahrenheit. Exercises: Convert the following; a. 80 inches to centimeters b. 200 centimeters to inches c. 55 kilograms to pounds d. 180 pounds to kilograms
Posted on: Wed, 14 Jan 2015 03:26:13 +0000
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