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Math Help - Rounding woes

  1. #1
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    Rounding woes

    My answers always seem to be off by about 10 cents and I know it has to do with my rounding. I normally try not to round off my figures until I reach the end of the equation but I thought that when dealing with dollars and cents, you're supposed to round things off or try to keep all figures with the same amount of decimal places. Whatever way it is, I'd like to know exactly how I'm supposed to know how many decimal places to keep.

    Here's the question I'm working on:
    Mr. Parker structured his will so that each of his four children will receive half as much from the proceeds of his estate as his wife, and each of 13 grandchildren will receive 1/3 as much as each child. After his death, $759,000 remains after expenses and taxes for distribution among his heirs. How much will each child and grandchild receive?

    My work:
    Total $ left to wife = x
    Total $ left to each child = 0.5x
    Total $ left to each grandchild = (1/3)(0.5x)

    Total $ in will = Total $ left to wife + Total $ left to children + Total $ left to grandchildren.
    1) $759,000 = x + 4(0.5x) + 13((1/3)(0.5x))
    2) $759,000 = x +2x + 2.1667x
    3) x = $759,000/5.1667 = $146,902.2781 left to wife
    therefore $ left to each child = 0.5($146,902.2781) = $73,451.1391

    (correct answer for $ left to each child is supposed to be $73.451.62. I purposely didn't round off in my work here. When I round the 1/100th decimal place in all places or various places, I still don't get exactly the right cents amount.

    Can any of you guys tell me a reliable method of rounding when it comes to this stuff? I've never been able to master it.
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  2. #2
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    Quote Originally Posted by greatsheelephant View Post
    My answers always seem to be off by about 10 cents and I know it has to do with my rounding. I normally try not to round off my figures until I reach the end of the equation but I thought that when dealing with dollars and cents, you're supposed to round things off or try to keep all figures with the same amount of decimal places. Whatever way it is, I'd like to know exactly how I'm supposed to know how many decimal places to keep.

    Here's the question I'm working on:
    Mr. Parker structured his will so that each of his four children will receive half as much from the proceeds of his estate as his wife, and each of 13 grandchildren will receive 1/3 as much as each child. After his death, $759,000 remains after expenses and taxes for distribution among his heirs. How much will each child and grandchild receive?

    My work:
    Total $ left to wife = x
    Total $ left to each child = 0.5x
    Total $ left to each grandchild = (1/3)(0.5x)

    Total $ in will = Total $ left to wife + Total $ left to children + Total $ left to grandchildren.
    1) $759,000 = x + 4(0.5x) + 13((1/3)(0.5x))
    2) $759,000 = x +2x + 2.1667x
    3) x = $759,000/5.1667 = $146,902.2781 left to wife
    therefore $ left to each child = 0.5($146,902.2781) = $73,451.1391

    (correct answer for $ left to each child is supposed to be $73.451.62. I purposely didn't round off in my work here. When I round the 1/100th decimal place in all places or various places, I still don't get exactly the right cents amount.

    Can any of you guys tell me a reliable method of rounding when it comes to this stuff? I've never been able to master it.
    You won't with rounding, the whole idea of rounding is to make answers easier to read, in the case of money you'll see utility companies using three decimal places in your bill but transactions are only ever 2 dp.

    Round only at the very end of a calculation. Modern calculators have a fraction button so you can use fractions instead of decimals.

    Spoiler:
    For example you mention that 13 \times \frac{1}{6}x = 2.1667x<br />
. It is better to leave that as \frac{13}{6}x


    Your setup is good as is your working

    759000 = x+ 2x + \frac{13x}{6}

    (Because \frac{1}{3} \times 0.5 = \frac{1}{6})


    6 is our common denominator so multiply everything by 6

    4554000 = 6x+12x+13x

    31x = 4554000

    x = \frac{4554000}{31} = 146903.23

    The wife gets $146903.23

    Each child gets \frac{4554000}{62} = 73451.61.

    (Note that I have used the fractional form of x)

    Each grandchild gets \frac{4554000}{31 \times 6} = 24483.87


    Adding the fractional values together:

    \left(13 \times \frac{4554000}{31 \times 6} \right) + \left( 4 \times \frac{4554000}{31 \times 2} \right) + \left(\frac{4554000}{31}\right) =759000 which is the original amount.

    Adding the rounded values

    146903.23 + 4 \times 73451.61 + 13 \times 24483.87 = 758999.98 which is 2 cents short.
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