Understanding Order of Magnitude in Mathematics: Symbol O Explained

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In summary, Order of magnitude is a mathematical concept that indicates the size of something in powers of ten within a factor of ten. It is often used to compare the magnitude of two quantities, with phrases like "X exceeds Y by n orders of magnitude" or "X is within n orders of magnitude of Y". The symbol O is used to represent orders of magnitude in equations, indicating that terms to the third power or higher have been dropped.
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In maths, what is meant by Order of magnitude, symbol O .
 
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Orders of magnitude indicate the size of something in powers of ten within a factor of ten. For example;

By "X exceeds Y by n orders of magnitude" is meant that X is at least 10^n but less than 10^(n+1) times greater than Y.

By "X is within n orders of magnitude of Y" is meant X is less than 10^(n+1) but greater than 10^-(n+1) times Y.
 
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  • #3
If you see an expression like

Y(t)=1+t+t^2+O(t^3)

The O means that there are terms to the third power and higher that are drop.

JMD
 
  • #4
Originally posted by nbo10
If you see an expression like

Y(t)=1+t+t^2+O(t^3)

The O means that there are terms to the third power and higher that are drop.

JMD

This is different than order of magnitude.
 

1. What is the meaning of order of magnitude in mathematics?

The order of magnitude in mathematics refers to the scale or size of a number or value. It is used to categorize numbers into different levels of magnitude, such as ones, tens, hundreds, thousands, etc. It helps to understand the relative size of numbers and make calculations and comparisons easier.

2. How is order of magnitude represented in mathematics?

The order of magnitude is represented using the symbol "O" or "o". This symbol is placed in front of a number to indicate that it is an approximate value and to show the level of magnitude. For example, 10,000 can be represented as O(104) to indicate that it is in the thousands magnitude.

3. What is the purpose of using order of magnitude in mathematics?

The purpose of using order of magnitude in mathematics is to simplify complex numbers and make them easier to work with. It also helps in understanding the relative size of numbers and making comparisons between them. It is particularly useful when dealing with very large or very small numbers in fields such as astronomy, physics, and economics.

4. How is order of magnitude calculated?

The order of magnitude is calculated by determining the number of digits in a number and then rounding it to the nearest power of 10. For example, if a number has 5 digits, it would be rounded to the nearest power of 10, which is 105 or 100,000. This would be represented as O(105).

5. How is order of magnitude used in scientific notation?

Order of magnitude is used in scientific notation to represent very large or very small numbers in a more compact and manageable form. In scientific notation, the first part of the number is a decimal between 1 and 10, and the second part is a power of 10. For example, 0.000005 can be written as 5 x 10-6, with an order of magnitude of O(10-6).

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