Error interval
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What minimum number can be rounded up to 2000 to 1 significant figure - minimum value?
What maximum number can be rounded down to 2000 to 2 significant figure - maximum value .
Please show us what you have tried and exactly where you are stuck.
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Please share your work/thoughts about these problems.
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Steven G
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How do you round off a number to 1 significant figure? How about 2 significant figures.
D
Deleted member 4993
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You reported 4 numbers!
Please explain these numbers.
You needed to figure out two numbers and calculate the third one from those two.
Please explain your work!
Dr.Peterson
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I'm not sure what your work means; it needs some explanation. I think maybe what you are saying is that the largest number that rounds to 2000, to one sig fig, is 2499, and the smallest is 1500. That's true. So the exact number of that crowd might be 2499.
Then you are saying that the largest number that rounds to 2000 to 2 sig figs is 2049, and the smallest is 1950. That is true too. So maybe the exact number of that crowd is 1950.
Then the difference between the two exact numbers is 2499 - 1950 = 549.
Do you think that might be the answer to the problem?
Yes. I wrote 549 as answer and its right.
Thank you. I was confused about EXACT number of people but now i can see what it means.
I am somewhat mystified by the question that spawned this thread.
I think that “exact” is, as the OP said, the word that requires initial explication. I also think that the question is slightly deceptive without the concepts of negative numbers and absolute value.
Rounded number A - Rounded number B = 2000 - 2000 = 0. But those are not NECESSARILY the true values. “Exact” in this question means “true.” Moreover, we are not asked to find those true numbers, but rather the maximum absolute value of the true difference between the true numbers, a question that would never occur to a student of arithmetic and completely disguises the issue of range of error. There are 1099 possible values for the difference between the pop crowd and the rock crowd rather than 550. The concept of range of error is implicitly misstated.
The question is a lot more pertinent for a student who has been introduced to algebra. (A lot of what are posed as arithmetic problems in later years seems to me to be very simple algebra problems. That suggests teaching algebra earlier.)
[MATH]1500 \le x \le 2499 \text { and } 1950 \le y \le 2049 \implies \\ - 2499 \le - x \le - 1500 \text { and } 1950 \le y \le 2049 \implies \\ 1950 - 2499 \le y - x \le 2049 - 1500 \implies - 549 \le y - x \le + 549.[/MATH]Now from that we get the correct answer [MATH]|\ y - x \ | \le 549.[/MATH]
But the technically correct answer to the question asked leaves the student with the false impression that the true difference must be non-negative because the student has no clue about negative numbers and absolute value. The student is mislead as to the range of potential error in the difference in size between one crowd and another. Why is this a useful question to pose?
EDIT: You may say that the question does not implicitly ask about the absolute value function but rather about the maximum value function. But of what possible value is it to ask about maximum value without asking about minimum value when the topic is error propagation.
I think that “exact” is, as the OP said, the word that requires initial explication. I also think that the question is slightly deceptive without the concepts of negative numbers and absolute value.
Rounded number A - Rounded number B = 2000 - 2000 = 0. But those are not NECESSARILY the true values. “Exact” in this question means “true.” Moreover, we are not asked to find those true numbers, but rather the maximum absolute value of the true difference between the true numbers, a question that would never occur to a student of arithmetic and completely disguises the issue of range of error. There are 1099 possible values for the difference between the pop crowd and the rock crowd rather than 550. The concept of range of error is implicitly misstated.
The question is a lot more pertinent for a student who has been introduced to algebra. (A lot of what are posed as arithmetic problems in later years seems to me to be very simple algebra problems. That suggests teaching algebra earlier.)
[MATH]1500 \le x \le 2499 \text { and } 1950 \le y \le 2049 \implies \\ - 2499 \le - x \le - 1500 \text { and } 1950 \le y \le 2049 \implies \\ 1950 - 2499 \le y - x \le 2049 - 1500 \implies - 549 \le y - x \le + 549.[/MATH]Now from that we get the correct answer [MATH]|\ y - x \ | \le 549.[/MATH]
But the technically correct answer to the question asked leaves the student with the false impression that the true difference must be non-negative because the student has no clue about negative numbers and absolute value. The student is mislead as to the range of potential error in the difference in size between one crowd and another. Why is this a useful question to pose?
EDIT: You may say that the question does not implicitly ask about the absolute value function but rather about the maximum value function. But of what possible value is it to ask about maximum value without asking about minimum value when the topic is error propagation.
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