 |
       |
|
|
|
|
| Become an SVP lifetime member SVPMembership |
 |
| The Do-It-Yourself Unincorporated Business Trust |
|
Topic: Dale Pond
Collected Articles Section: Ratios and Proportion Table of Contents to this Topic |
|
Ratios and Proportion by Dale Pond 2004, 04/14 There are many ways of discussing ratios and proportions. One way that works for me is to read a ratio as "parts". In the ratio 2:1, read two parts to one part. Or in practical terms two measures of a substance to one measure of another substance. Let's say two teaspoons of sugar to one teaspoon of butter. In vibration studies the "unit of measure" may be either frequency (cycles per second) or time (wave number) or space (wave length). So the ratio of 2:1 refers to either of these "units of measure" meaning the first term (2) is TWICE the value of the second term (1). Or reciprocally we can say the second term is HALF the value of the first. Ratios are nearly always (but not always!) reduced to their least common factors. Hence if we had a ratio of 200:100 or 4:2 it would usually be reduced to 2:1 to keep things simple. So if there is another ratio of 4:7 it would mean 4 parts to 7 parts. We can multiply the 4 and 7 respectively times anything we want: bushels, teaspoons, inches, cycles per second or whatever. The important thing is the final result must always be the same PROPORTION of 4 to 7. An additional thing to remember is to avoid reducing the ratio to a decimal. Sometimes reducing it to a decimal can be helpful but the decimal is NOT the original ratio. Another problem is a whole number ratio represents whole number quantities of two distinctly different things. So the reduction to a decimal is the same thing as dividing apples by oranges. This is not something most people see and understand. They've been mistaught in school to always reduce to a decimal. And this, in my opinion, is a grave error. We see this tendency quite often in the reduction of the ratio of 20612 : 6561 which is the ratio of the parts of a circumference of a circle (curved line) to the parts of length of that circle's diameter (straight line). These two numbers represent whole number values of two distinctly different things. How could they be divided and still have accuracy? Not possible - one ends up with an APPROXIMATION which is a value acknowledged to have an error. Adding more decimals does not eliminate the error, it is simply reduced. |
| See Also: |
 |
 |
|
 |
 |
