Are 3.4 and 0.1 in the same order of magnitude?

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For example, 3.4 and 0.1 are within an OoM of each other because 3.4/0.1=34<10. But 3.4 and 0.001 are not within an OoM of each other because 3.4/0.001=3400>10. In summary, the order of magnitude for a number is determined by its power of ten in standard form and is a measure of its scale. When comparing two numbers, their order of magnitude can be determined by looking at their ratios and seeing if the larger ratio is smaller than 10. However, there can be some variation and fudge factor involved in determining the exact order of magnitude.
  • #1
billabuwl50
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are 3.4 and .1 in the same order of magnitude
 
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  • #2
That depends on how exactly you defined an order of magnitude.
Does http://en.wikipedia.org/wiki/Orders_of_magnitude" help you?
 
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  • #4
So, does the entire number make up the order of magnitude or just the decimal places.
 
  • #5
Just the decimal places? I think 8.5 and 8.47395 are of the same order of magnitude, but the decimal places are respectively 1 and 5...
 
  • #6
billabuwl50 said:
are 3.4 and .1 in the same order of magnitude
From my understanding after reading the wikipedia article 0.1 is of magnitude -1 while 3.4 has an order of magnitude of 0. To work out the order of magnitude you can write the number in standard form, the power of ten when it is in standard form is the magnitude.

An order of magnitude difference is different though. 3.4 is 34 times as big as 0.1, so it is two orders of magnitude bigger (round log34 to the nearest integer).

This is just my understanding from quickly reading the wikipedia article, so what I've said should be taken with a pich of salt (as should anything from wikipedia).

Edit: Gokul43201 pointed out an error I made. I think it is now correct (though you still shouldn't assume that everything I've said is completely accurate).
 
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  • #7
billabuwl50 said:
So, does the entire number make up the order of magnitude or just the decimal places.
Order of Magnitude tells you the Scale of a number. Decimal places is about Precision.

[tex]x=2.17\;y=3.38613[/tex]

x and y have the same Order of Magnitude, but y has more Precision.
 
  • #8
raoulh said:
(round 34 to the nearest power of ten and take the index)
When talking orders of magnitude or anything involving comparisons in terms of factors (ratios being more important than differences), you do not round off arithmetically - you round off numbers geometrically.

Also, what's important with OoMs is the word "about" you find in the mathworld definition - there's fudge factor involved. But if you want to go with a purist definition of an OoM, (which is a silly waste of time, in my opinion) two numbers are within an OoM of each other if the larger ratio of the numbers(b/a, if b>a) is smaller than 10.
 

FAQ: Are 3.4 and 0.1 in the same order of magnitude?

What is the significance of "Order of Magnitude: 3.4 & 0.1"?

The term "order of magnitude" refers to the scale or size of a quantity, typically measured in powers of 10. In this case, the numbers 3.4 and 0.1 represent two different orders of magnitude.

How do you calculate the order of magnitude?

To calculate the order of magnitude of a number, count the number of digits in the number and then subtract 1. For example, the number 3.4 has 2 digits, so its order of magnitude is 2-1=1.

What is the difference between 3.4 and 0.1 in terms of order of magnitude?

The difference between 3.4 and 0.1 in terms of order of magnitude is one. This means that 3.4 is one order of magnitude larger than 0.1.

Why is order of magnitude important in scientific calculations?

Order of magnitude is important in scientific calculations because it allows us to quickly estimate the size or scale of a quantity without having to calculate the exact value. This is useful when dealing with very large or very small numbers.

Can order of magnitude be used for non-numerical quantities?

Yes, order of magnitude can be used for non-numerical quantities such as measurements of time or distance. In these cases, the order of magnitude refers to the scale or size of the quantity being measured.

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