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Math Help - How is this inaccurate?

  1. #1
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    How is this inaccurate?

    Hello,

    I've been confronted by a parent who stated that my statements below are wrong

    Please can you advise why?

    Use four digit whole numbers with two decimal places..
    4567.89 rounded equals 4567.9 then 4568.0

    9876.54 rounded equals 9876.50 then 9877.0
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  2. #2
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    Re: How is this inaccurate?

    Quote Originally Posted by Connie View Post
    I've been confronted by a parent who stated that my statements below are wrong
    Please can you advise why?
    Use four digit whole numbers with two decimal places..
    4567.89 rounded equals 4567.9 then 4568.0

    9876.54 rounded equals 9876.50 then 9877.0
    I see nothing wrong with the statements.
    But all depends upon definition. How do you define rounding?
    It appears that by round you mean to the closest integer.
    If that is the case, and the decimal part is at least half round up.
    Thanks from topsquark
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  3. #3
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    Re: How is this inaccurate?

    Quote Originally Posted by Plato View Post
    I see nothing wrong with the statements.
    But all depends upon definition. How do you define rounding?
    It appears that by round you mean to the closest integer.
    If that is the case, and the decimal part is at least half round up.
    Thank you for your prompt response.

    The individual stated that my use of the word equals was wrong.
    Then they commented that the statement '4567.89 rounded equals 4567.9' was incorrect.

    To put this in context this was the text that I sent home:
    Your maths mission for this week is to practise and improve your skills at rounding numbers to the nearest 1, 10, 100, or 1000.

    Remember, when using whole numbers, look at the units. If the unit value equals 0 or 1 or 2 or 3 or 4 (less than 5) then round down:
    72 rounded equals 70 because the 2 units is less than 5
    654 rounded equals 650 because the 4 units is less than 5
    9753 rounded equals 9750 because the 3 units is less than 5

    If the unit value equals 5 or 6 or 7 or 8 or 9 (more than 4) then round up:
    56 rounded equals 60 because the 6 units is more than 4
    345 rounded equals 350 because the 5 units is more than 4
    4567 rounded equals 4570 because the 7 units is more than 4

    If you want a challenge then use four digit whole numbers with two decimal places.
    4567.89 rounded equals 4567.9 then 4568.0
    9876.54 rounded equals 9876.50 then 9877.0
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  4. #4
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    Re: How is this inaccurate?

    Quote Originally Posted by Connie View Post
    Thank you for your prompt response.
    The individual stated that my use of the word equals was wrong.
    Then they commented that the statement '4567.89 rounded equals 4567.9' was incorrect.
    To put this in context this was the text that I sent home:
    Your maths mission for this week is to practise and improve your skills at rounding numbers to the nearest 1, 10, 100, or 1000.
    Remember, when using whole numbers, look at the units. If the unit value equals 0 or 1 or 2 or 3 or 4 (less than 5) then round down:
    72 rounded equals 70 because the 2 units is less than 5
    654 rounded equals 650 because the 4 units is less than 5
    9753 rounded equals 9750 because the 3 units is less than 5
    If the unit value equals 5 or 6 or 7 or 8 or 9 (more than 4) then round up:
    56 rounded equals 60 because the 6 units is more than 4
    345 rounded equals 350 because the 5 units is more than 4
    4567 rounded equals 4570 because the 7 units is more than 4
    If you want a challenge then use four digit whole numbers with two decimal places.
    4567.89 rounded equals 4567.9 then 4568.0
    9876.54 rounded equals 9876.50 then 9877.0
    Frankly, I would avoid both the words rounded and equals.
    I would ask, "what is the closest integer?".
    On the other hand, the statement "The rounded form of 456.9 equals 457" is a very clear use of both words.
    Thanks from topsquark
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  5. #5
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    Re: How is this inaccurate?

    Can we say "72 rounded off is equal to 70?"
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    Re: How is this inaccurate?

    Quote Originally Posted by aldrincabrera View Post
    Can we say "72 rounded off is equal to 70?"
    No because 72 is an integer.
    Again, what is the working definition of "to round"?
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  7. #7
    Member aldrincabrera's Avatar
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    Re: How is this inaccurate?

    Per merriam-webster round means "to express as a round number —often used with off." I am also confused with merriams example : "11.3572 rounded off to two decimal places becomes 11.36."
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    Re: How is this inaccurate?

    Thanks for those that have responded.

    So, have I been mathematical incorrect in using the term equals within the sentence:

    4567.89 rounded equals 4567.9 then 4568.0
    Thanks from Plato
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  9. #9
    Forum Admin topsquark's Avatar
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    Re: How is this inaccurate?

    Quote Originally Posted by Connie View Post
    Thanks for those that have responded.

    So, have I been mathematical incorrect in using the term equals within the sentence:

    4567.89 rounded equals 4567.9 then 4568.0
    Out of curiosity why are you rounding in two steps? You can round 4567.89 to 4568 in one step.

    -Dan
    Thanks from Plato
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  10. #10
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    Re: How is this inaccurate?

    Quote Originally Posted by topsquark View Post
    Out of curiosity why are you rounding in two steps? You can round 4567.89 to 4568 in one step.

    -Dan
    This homework is for children of age 9. In class we were practising the method of rounding and recorded their answers in this format:

    1234.56
    1234.60
    1235.0
    1240
    1200
    1000

    This is mathematically acceptable, isn't it?
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  11. #11
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    Re: How is this inaccurate?

    Quote Originally Posted by Connie View Post
    This homework is for children of age 9. In class we were practising the method of rounding and recorded their answers in this format:

    1234.56
    1234.60
    1235.0
    1240
    1200
    1000

    This is mathematically acceptable, isn't it?
    Well, if they rounded to the nearest 10 at the beginning, they would have gotten 1230 instead of 1240.
    Thanks from topsquark
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  12. #12
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    Re: How is this inaccurate?

    Thanks for your response.

    In class they were taught to round to the next place value position, and so for 1234.56 I would have expected to see, 1234.6.
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  13. #13
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    Re: How is this inaccurate?

    There is nothing mathematically inaccurate about the algorithm you are teaching. But, that algorithm produces results that are undesirable in practical applications. Let's consider rounding to the unit, and compare the algorithm you are teaching to the algorithm of rounding to the nearest unit. For numbers with one digit after the decimal point, both algorithms yield the same results. For numbers with two digits after the decimal point, numbers ending with .45 to .49 round up using the algorithm you are teaching while they round down when rounding to the nearest unit. Assuming that in some practical application, numbers have equal chances of ending with any two digits, there is a 5% chance that any given number will round up using the algorithm you are teaching and down otherwise. Depending on the application, that can produce extremely significant differences in results.
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