Unit Conversions

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The monthly advisory fee for an account with $100,000 is as follows: $1000,000 * 0.0025 * 30/365 = $20.55

How would this calculation appear using dimensional analysis? Are any of the following correct?

$100,000 * (12 months)/year * 0.0025/month * (30/365) year, or is it $100,000/month * 12 month/year * 0.0025 * (30/365) year?



What about this example. Determine the interest on $635 for 6 days at 6% using 360 days for the year.

$635 * $0.06/year * 1 year/360 days * 6 days = $0.635, or is it $635/year * $0.06 * 1 year/360 days * 6 days = $0.635?



What about the following: The sales tax for a taxable item is 7%. What is the tax on two items?

$0.07/$1.00 * $1.00 /1 item * 2 items = $0.07 * 2 = $0.14
 

Subhotosh Khan

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The monthly advisory fee for an account with $100,000 is as follows: $1000,000 * 0.0025 * 30/365 = $20.55

How would this calculation appear using dimensional analysis? Are any of the following correct?

$100,000 * (12 months)/year * 0.0025/month * (30/365) year, or is it $100,000/month * 12 month/year * 0.0025 * (30/365) year?



What about this example. Determine the interest on $635 for 6 days at 6% using 360 days for the year.

$635 * $0.06/year * 1 year/360 days * 6 days = $0.635, or is it $635/year * $0.06 * 1 year/360 days * 6 days = $0.635?



What about the following: The sales tax for a taxable item is 7%. What is the tax on two items?

$0.07/$1.00 * $1.00 /1 item * 2 items = $0.07 * 2 = $0.14
You state:

The monthly advisory fee for an account with $100,000 is as follows: $1000,000 * 0.0025 * 30/365 = $20.55​

What is the "dimension" of 0.0025? - I think it should be "per year"!

In my opinion, the calculation should be (since you are calculating fee/month):

fee = 100000 [$] * (1/12) [year/month] * 0.0025 [/year] = 250/12 [$/month] =20.83 [$/month]
 

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I thank you for your reply!

What about my other examples? Are they incorrect?
 

Dr.Peterson

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What about this example. Determine the interest on $635 for 6 days at 6% using 360 days for the year.

$635 * $0.06/year * 1 year/360 days * 6 days = $0.635, or is it $635/year * $0.06 * 1 year/360 days * 6 days = $0.635?
A percentage is dimensionless, so the "$" is wrong on it. Make this

$635 * 0.06/year * 1 year/360 days * 6 days = $0.635​

Now the units work out. Your second option is inappropriate because the $635 is not an amount per year, but a one-time principal.

Questions like these are generally answered just by looking at what the individual numbers mean in the problem.

What about the following: The sales tax for a taxable item is 7%. What is the tax on two items?

$0.07/$1.00 * $1.00 /1 item * 2 items = $0.07 * 2 = $0.14
I would just say the tax is 7% of the price of the item; and since you haven't been told what that price is, we can't answer the question.
 

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A percentage is dimensionless, so the "$" is wrong on it. Make this

$635 * 0.06/year * 1 year/360 days * 6 days = $0.635​

Now the units work out. Your second option is inappropriate because the $635 is not an amount per year, but a one-time principal.

Questions like these are generally answered just by looking at what the individual numbers mean in the problem.


I would just say the tax is 7% of the price of the item; and since you haven't been told what that price is, we can't answer the question.
I want to thank you for the reply.

1. The price is $1.00 per item and the purchase is for two items at 7%. 0.07 * $1.00/item * 2 items = $0.14 Why is this incorrect?

2. Do I understand correctly that expressing the percentage of 7% as $0.07/$1.00 as I have done in my first posting is not correct? I changed it to 0.07 in 1. in this posting since you indicated that percentages have no units or are dimensionless..
 
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Dr.Peterson

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1. The price is $1.00 per item and the purchase is for two items at 7%. 0.07 * $1.00/item * 2 items = $0.14 Why is this incorrect?
I didn't say your answer was incorrect; I said that the problem as you stated it didn't mention the price!

I would just say that the price is 2 * $1.00 = $2.00, and the tax is 7% of that, which is 0.07*$2.00 = $0.14. There is no need to apply dimensional analysis, unless you want to.

2. Do I understand correctly that expressing the percentage of 7% as $0.07/$1.00 as I have done in my first posting is not correct? I changed it to 0.07 in 1. in this posting since you indicated that percentages have no units or are dimensionless.
$0.07/$1.00 is dimensionless, as the dollars cancel out. It means exactly the same thing as 0.07 (or 7%, for that matter).

You seem to be assuming that if someone doesn't explicitly say you are right, they are saying you are wrong. You are wrong about that!
 

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:
I would just say that the price is 2 * $1.00 = $2.00, and the tax is 7% of that, which is 0.07*$2.00 = $0.14. There is no need to apply dimensional analysis, unless you want to.

I wanted to just to see whether or not I have done so correctly. I like seeing calculations with units. So, I am still somewhat confused.
Is the following correct using units, yes or no? 0.07 * $1.00/item * 2 items = $0.14
 

Dr.Peterson

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I wanted to just to see whether or not I have done so correctly. I like seeing calculations with units. So, I am still somewhat confused.
Is the following correct using units, yes or no? 0.07 * $1.00/item * 2 items = $0.14
Look fine to me; everything means what it should, and cancels to give the units of the result.
 

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I want to thank you for the replies and comments!
 

Jomo

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In the 1st part of your original post, where is the 12 coming from??
 

Explain this!

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In the 1st part of your original post, where is the 12 coming from??
If you are referring to the following: $100,000 * (12 months)/year * 0.0025/month * (30/365) year, the 12 is the 12 months in one year. The 12 months/1 year is the conversion factor used in this solution.

If I did not answer your question, let me know!
 

Jomo

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If you are referring to the following: $100,000 * (12 months)/year * 0.0025/month * (30/365) year, the 12 is the 12 months in one year. The 12 months/1 year is the conversion factor used in this solution.

If I did not answer your question, let me know!
Your 1st equation had no 12 but now I realized that in your 2nd equation you put 12 month per year which is equivalent to 1.
 

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Your 1st equation had no 12 but now I realized that in your 2nd equation you put 12 month per year which is equivalent to 1.
If I understand your reply correctly, the 12 months/year cancel out from the other units in the equation. Is this what you are refering to?
The very first equation does not use any units except the dollar sign ($).
 

JeffM

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We ask for one problem per thread. It becomes very unclear what you are talking about over 13 posts.

Your first problem is unclear: "how would you calculate THIS." What is the "this" that we are to calculate?

Is it the annual fee?. Why 30 day/ 365 days? A month is not always 30 days. If you have a monthly fee and are interested in a year, why mess around with days at all.

Is it 1000.00, 100,000.00, or 1,000,000.00? If, as it seems, it is 100,000 * 0.0025 = 250.

\(\displaystyle \dfrac{12 \text { months}}{\text {year}} * \dfrac{\dfrac{250 \text { dollars in fees}}{100,000 \text { dollars in value}}}{\text {month}} =\)

\(\displaystyle \dfrac{\dfrac{3000 \text { dollars in fees}}{100000 \text { dollars in value}}}{\text {year}}.\)

When you are working with monetary units, you have to clarify your dimensions with dollars worth of what?
 

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We ask for one problem per thread. It becomes very unclear what you are talking about over 13 posts.

Your first problem is unclear: "how would you calculate THIS." What is the "this" that we are to calculate?

Is it the annual fee?. Why 30 day/ 365 days? A month is not always 30 days. If you have a monthly fee and are interested in a year, why mess around with days at all.

Is it 1000.00, 100,000.00, or 1,000,000.00? If, as it seems, it is 100,000 * 0.0025 = 250.

\(\displaystyle \dfrac{12 \text { months}}{\text {year}} * \dfrac{\dfrac{250 \text { dollars in fees}}{100,000 \text { dollars in value}}}{\text {month}} =\)

\(\displaystyle \dfrac{\dfrac{3000 \text { dollars in fees}}{100000 \text { dollars in value}}}{\text {year}}.\)

When you are working with monetary units, you have to clarify your dimensions with dollars worth of what?
I want to thank you for your reply!

You replied as follows:

"We ask for one problem per thread. It becomes very unclear what you are talking about over 13 posts."

Yes, some of the time the experts ask for clarification and the response may require a shift from the original question.

"Your first problem is unclear: "how would you calculate THIS." What is the "this" that we are to calculate?"

There is nothing to calculate. I did not ask for an answer to any calculations that I posted.

"Is it the annual fee?. Why 30 day/ 365 days? A month is not always 30 days. If you have a monthly fee and are interested in a year, why mess around with days at all."

No, it is not an annual fee. It is a monthly advisory fee that is charged after each month. If the month does not have 30 days, use 31 days.

"Is it 1000.00, 100,000.00, or 1,000,000.00? If, as it seems, it is 100,000 * 0.0025 = 250."

I think it is clear in my first posting that it is $100,000 * 0.0025 * 30/365.

I am merely interested dimensional analysis of this problem and others similar to it.
 

JeffM

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You still do not say what ”this” is. What are you trying to calculate?

Nor do you say what 30/365 has to do with anything?

If you rent an apartment for 1500 per month, it is 1500 each month even though the majority of months do not contain 30 days, nor do all years contain 365 days. Per month means per month, not something else.

And $100,000 * 00.0025 = 250.

So virtually nothing about your postis clear.

If you simply want to know how to express the fee in units, it is, AS I PREVIOUSLY EXPLAINED,

\(\displaystyle \dfrac{\dfrac{250 \text { dollars in fees}}{100,000 \text { dollars under management}}}{\text {month}}.\)
 

Explain this!

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You still do not say what ”this” is. What are you trying to calculate?

Nor do you say what 30/365 has to do with anything?

If you rent an apartment for 1500 per month, it is 1500 each month even though the majority of months do not contain 30 days, nor do all years contain 365 days. Per month means per month, not something else.

And $100,000 * 00.0025 = 250.

So virtually nothing about your postis clear.

If you simply want to know how to express the fee in units, it is, AS I PREVIOUSLY EXPLAINED,

\(\displaystyle \dfrac{\dfrac{250 \text { dollars in fees}}{100,000 \text { dollars under management}}}{\text {month}}.\)
I want to thank you for the reply. See Subhotosh Khan's calculation above.

Have a good day!
 
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