Failed to understand "the number of magnitudes that the quantities differ is specified to within..."

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Would you like to explain the meaning of "the number of magnitudes that the quantities differ is specified to within a power of 10"? For instance, use more details and examples to explain it.

Context:

order of magnitude
n.
1. a degree in a continuum of size or quantity
2. a number assigned to the ratio of two quantities; two quantities are of the same order of magnitude if one is less than 10 times as large as the other; the number of magnitudes that the quantities differ is specified to within a power of 10

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Type: Question • Score: 3 • Views: 445 • Replies: 8

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View best answer, chosen by oristarA

@oristarA,

It merely means that an order of magnitude difference between two quantities can be no more than ten times per order of magnitude. One order of magnitude is 10 times greater or 10^1, two orders of magnitude is one hundred times greater or 10^2, three orders of magnitude is one thousand times greater or 10^3.
Its just a base 10 logarithmic description of comparison of quantity.

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@farmerman,

farmerman wrote:

It merely means that an order of magnitude difference between two quantities can be no more than ten times per order of magnitude. One order of magnitude is 10 times greater or 10^1, two orders of magnitude is one hundred times greater or 10^2, three orders of magnitude is one thousand times greater or 10^3.
Its just a base 10 logarithmic description of comparison of quantity.

Thank you Farmerman.

Please be more concrete. For example:
Quantity A: 19
Quantity B: 99999

So an order of magnitude difference (one order of magnitude difference)between A and B is no more than ten times?

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@oristarA,

you do it (thats how teachers work).
Make an approximate log quantity for each

19 is about 1.9X10^1

what is 99999?

Then just subtract A from B (log value) and that is the approximate orders of magnitude difference

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@oristarA,

Shouldn't that read, "…by which the quantities differ…."

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@farmerman,

farmerman wrote:

you do it (thats how teachers work).
Make an approximate log quantity for each

19 is about 1.9X10^1

what is 99999?

Then just subtract A from B (log value) and that is the approximate orders of magnitude difference

99999 is about 9.9999X10^4

4-1=3.
That is, 99999 is 3 order of magnitudes more larger than 19.
Am I on the right track?

1 Reply

@oristarA,

oristarA wrote:

order of magnitudes

orders of magnitude (note placement of plural 's')

You are on the right track.

99999 is 3 orders of magnitude greater than 19

1 Reply

@contrex,

contrex wrote:

oristarA wrote:
order of magnitudes

orders of magnitude (note placement of plural 's')

You are on the right track.

99999 is 3 orders of magnitude greater than 19

Thank you.
In "the number of magnitudes that the quantities differ is specified to within a power of 10," magnitudes refers to "orders of magnitude"?

1 Reply

@oristarA,

oristarA wrote:

In "the number of magnitudes that the quantities differ is specified to within a power of 10," magnitudes refers to "orders of magnitude"?

I think "number of magnitudes" may be an error, possibly by a non-native speaker, or at least a very non-customary usage. I am more used to seeing "order (or orders) of magnitude".

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Failed to understand "the number of magnitudes that the quantities differ is specified to within..."

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