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Deleted member 4993
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Your question was:
You should check your answer:
1.2 * 83.33 = 99.996
This can be rounded up to approximately 100 - but not exactly 100. You may want to ask the instructor for clarification.
1.2 * 83.33 = 99.996
This can be rounded up to approximately 100 - but not exactly 100. You may want to ask the instructor for clarification.
Incorrect. It gets rounded up to exactly 100. That's what rounding does here.
\(\displaystyle (\$83.33)(1.20) \ = \ \$99.996, \ \) which rounds up to exactly 100 dollars.
The student has no need to ask the instructor for clarification on this question.
mmm4444bot
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What did your mama teach you? Cut a penny into 1,000 equal pieces, and take 'em with you to the restaurant?
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Deleted member 4993
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Exact value of $100 is $100. Approximate value of $99.996 is approximately $100.
If a tax rate multiplied by the original price, added to the original price, equals a selling price between $99.995 and $100.0049..., inclusive,
then the selling price is exactly $100.
You are having difficulty with both English and arithmetic definitions/meanings.
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Deleted member 4993
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Shades of BigGlenTheHeavy (or prominent political figure) → when the technical argument is lost - start personal attack....
Wrong. There was no loss of a technical argument for lookagain. In fact, the technical argument was confirmed for lookagain here:
https://www.freemathhelp.com/forum/threads/106919-Tip-at-Restaurant-Question
A personal attack wasn't made. Your response to/about lookagain showed you not addressing your lack of a technical argument.
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Oh for goodness sake. Another tempest in a teapot started by lookagain.
As frequently happens, it is a dispute about words, about usage, and is completely irrelevant to the original question asked.
There is a mathematically exact answer to the original question, namely
\(\displaystyle \dfrac{100}{1.2}\) dollars.
That exact answer is meaningless for practical purposes because currency does not always permit exact division: one twelth of the value of a thousand dollars cannot be obtained exactly. To get a practically meaningful answer we must resort to approximations because 1.2 times any number exactly expressible to two decimal places cannot equal 100 exactly:
\(\displaystyle 83.33 * 1.2 = 99.996 < 100 < 100.008 = 83.34 * 1.2.\)
Moreover \(\displaystyle |100 - 1.2 * 83.33| < |100 - 1.2 * 83.34|.\)
So 83.33 is the best approximation that is useful for practical purposes.
Now SK's answer may be open to criticism as missing an opportunity to enlighten the student about the difference between pure and applied mathematics or to enlighten the student about what makes an approximation good or to enlighten the student on the use of rounding to create reasonable approximations. Whether the student would have appreciated such digressions is a different issue. If the student found SK's answer unsatisfactory or unclear, the student could have asked a question to follow up.
The result of rounding is usually an approximate answer to the underlying problem even though the rounding process always gives an exact decimal representation. That distinction is logically valid, but it is utterly irrelevant to anything asked by the student.
If I had thought it helpful to the student, I would have said that 83.33 was the approximation, not 100. 1.2 and 100 were givens. But that again is a distinction that would have been lost on the student and so is irrelevant.
As frequently happens, it is a dispute about words, about usage, and is completely irrelevant to the original question asked.
There is a mathematically exact answer to the original question, namely
\(\displaystyle \dfrac{100}{1.2}\) dollars.
That exact answer is meaningless for practical purposes because currency does not always permit exact division: one twelth of the value of a thousand dollars cannot be obtained exactly. To get a practically meaningful answer we must resort to approximations because 1.2 times any number exactly expressible to two decimal places cannot equal 100 exactly:
\(\displaystyle 83.33 * 1.2 = 99.996 < 100 < 100.008 = 83.34 * 1.2.\)
Moreover \(\displaystyle |100 - 1.2 * 83.33| < |100 - 1.2 * 83.34|.\)
So 83.33 is the best approximation that is useful for practical purposes.
Now SK's answer may be open to criticism as missing an opportunity to enlighten the student about the difference between pure and applied mathematics or to enlighten the student about what makes an approximation good or to enlighten the student on the use of rounding to create reasonable approximations. Whether the student would have appreciated such digressions is a different issue. If the student found SK's answer unsatisfactory or unclear, the student could have asked a question to follow up.
The result of rounding is usually an approximate answer to the underlying problem even though the rounding process always gives an exact decimal representation. That distinction is logically valid, but it is utterly irrelevant to anything asked by the student.
If I had thought it helpful to the student, I would have said that 83.33 was the approximation, not 100. 1.2 and 100 were givens. But that again is a distinction that would have been lost on the student and so is irrelevant.