Orders of Magnitude, Unit Prefixes
From High School Online Collaborative Writing
[edit] ORDERS OF MAGNITUDE
[edit] Purpose of Orders of Magnitude
Order of Magnitude is used to make approximate comparisons between numbers. To calculate the Order of Magnitude you need to know that the closest number of exponents in a value of 10 equals the Order of Magnitude. Orders of Magnitude are usually used to make comparisons, and produce general relationships between two values. It is never used to calculate precise values, or unequivocal answers. One Order of Magnitude is equal to 101. The chart below shows the relationship between multiples of 10, and Orders of Magnitude.
[edit] General rules, that calculate Orders of Magnitude
Calculating the Order of Magnitude is not a difficult procedure, just know that when calculating Orders of Magnitude, you follow similiar rules as scientific notation, and you only use 10 raised to an exponent. Generally the Order of Magnitude is equal to the exponent 10 is raised to, for example 3.4 * 103 would have an order magnitude of 3. The rules of scientific Notation show how when a number is raised to a certain number you multiply the number that has an exponent by itself by the amount of times specified in the exponent. For Example, 53=5*5*5=125. The same rules apply to Orders of Magnitude, just exclusively with values of 10.
[edit] How to round Orders of Magnitude
The exception to the rule that Orders of Magnitude are equal to the exponent that 10 is raised to, is when the mantissa is equal to or over 5. When the mantissa is 5 or larger than 5 you round up a power. This is because you want to calculate the approximate value so when the mantissa is over 5 its more like multiplying the power of 10 by another 10. For example 8.9* 104 value is closer to 105 than 104. 105 is equal to 100, 000, 104 is equal to 10,000 and 8.9* 104 is equal to 89,000. 89,000 is closer to 100,000 than 10,000. Therefore 8.9* 104 would have an Order of Magnitude of 5.
[edit] How to calculate the difference between two Orders of Magnitude
To calculate the difference in orders of magnitude, you just subtract the smaller Order of Magnitude from the other Order of Magnitude.The end value is still like a power of 10. For example a number with a magnitude of 8 , is 3 Orders of Magnitude larger than a number with an Order of Magnitude of 5. There for the order of the magnitude is 1000 times larger.
[edit] Real World Examples of how to use Orders of Magnitude for comparison
A real world example is an ant is approximately .00005* 10-2 m long and a human is approximately .000057* 105 tall. That means a human is 7 Order of Magnitude longer than an ant, or you can say that a human is 10,000,000 times larger. PICTURE EXAMPLE PICTURE
[edit] How to compose Orders of Magnitude using correct notation
Order of magnitude is immensely useful to find general ratios between two values, and how much larger or smaller things are. But in order to make accurate comparisons it is important to know the appropriate notation. You must know the rules of Scientific Notation in order to calculate the correct Order of Magnitude. For example if you want to find the approximate relationship between the numbers 2.167*106 and 25.4*108 saying that 25.4*108was relatively 2 order of magnitudes larger or 100 times larger than 2.167*106 would be inaccurate. A correct relationship would be between 2.167*106 and 2.54*109, you would say that 2.54*109 was about 3 order of magnitudes larger or 1000 times larger than 2.167*106. Always remind yourself when finding the ratio that they both must be in the same notation. CHART
[edit] Relationship between logarithms and Orders of Magnitude
Order of magnitude is closely related to logarithms. When calculating a logarithm you are calculating, when 10 is raised to what number, equals the number you are taking the log of. For example 10x= 10,000, so if you logged 10,000, the answer would be 3, so x=3,103= 10,000, so there for the Order of Magnitude would also equal 3. So if you take a log of a number, the logarithm would also be the Order of Magnitude of that number.
[edit] Rounding Orders of Magnitude, when using logaritms
The rules for rounding, discussed in relation to the matissa do not apply to the method of using logs to calculate the Order of Magnitude. Because when you round in terms of the Order of Magnitude based on the matissa you are only rounding it to closest power. Where if you round the exponent you are not rounding to the closest power. For Example Log of 4,000,000 equals approximately 6.602. meaning 106.602 equals to 4,000,000, and if written in scientific notation it would be 4.0* 106. The matissa is still under 5 there for this would still have an order of magnitude of 6. If you rounded the exponents you would have a wrong order of magnitude, you would have 4.0* 107 which is 40,000,000.
[edit] Reminders
When solving for magnitude you must know all the rules of Scientific Notation. You must know the order, the relationships, and steps of scientific notation. Use the relationship between logs, scientific notation, units of measurement, and Order of Magnitude to solve for the Order of Magnitude. And most importantly remember that Order of Magnitude is used for approximations and general relationships, not for precise calculations.
[edit] Unit Prefixes
[edit] Purpose, and list of basic prefixes
SI prefixes are used to define a number by dividing it into subvisions using prefixes. The main goal of a unit prefix is to simplify a number. The chart below displays the basic SI unit prefixes, and their alternate meanings.
