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Math Help - Comparing Percents, Decimals, and Fractions

  1. #1
    Hope
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    Comparing Percents, Decimals, and Fractions

    I am trying to help my daughter with her homework. I cannot remember how to change percents or decimals. Sad I know?!

    Her assignment is using greater than, less than, and equal. For example:

    62% 5/8 I can't remember the steps to figure out which is
    greater than, less than, or equal.

    0.9 9% This is another kind of example.

    ANY help would be appreciated. I am at a loss!

    Thank You!
    Hope
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  2. #2
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    Quote Originally Posted by Hope View Post
    I am trying to help my daughter with her homework. I cannot remember how to change percents or decimals. Sad I know?!

    Her assignment is using greater than, less than, and equal. For example:

    62% 5/8 I can't remember the steps to figure out which is
    greater than, less than, or equal.

    0.9 9% This is another kind of example.

    ANY help would be appreciated. I am at a loss!

    Thank You!
    Hope
    Percent means divided by 100.

    Thus, 62 \% =\frac{62}{100}
    And,
    \frac{5}{8}

    Commond denominator is 200.

    Multiply the first fraction by 2 and second 25.

    \frac{62}{100} \cdot \frac{2}{2} = \frac{128}{200}

    \frac{5}{8} \cdot \frac{25}{25} = \frac{125}{200}

    Thus, the first one is larger.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by Hope View Post
    I am trying to help my daughter with her homework. I cannot remember how to change percents or decimals. Sad I know?!

    Her assignment is using greater than, less than, and equal. For example:

    62% 5/8 I can't remember the steps to figure out which is
    greater than, less than, or equal.

    0.9 9% This is another kind of example.

    ANY help would be appreciated. I am at a loss!

    Thank You!
    Hope

    A) To change percent to decimals:

    Percent is "per century" or per hundred.
    So 62% = 62/100 = 0.62
    Or, as short cut, move the decimal point 2 places to the left.
    In 62, the decimal point is understood to be at the end of the number, after the 2. So move the not-shown decimal point to two places to the left. Past 2, past 6, so ----0.62.

    9% = 9/100 = 0.09
    Or, 9. ----move the decimal point two places to the left = .09 = 0.09

    B) To change decimals to percent:

    Reverse the procedure mentioned above. Now it is move the decimal point two places to the right.
    0.62 = 62%
    0.09 = 9%
    0.005 = 0.5%
    1.5943 = 159.43%

    To change a fraction to decimals, just divide the numerator by the denominator.
    5/8 = 5 divided by 8 = 0.625
    If you want that in percent, you move the decimal point to two plces to the right, thus, 0.625 = 62.5%

    -----------------------------------------
    Compare 62% and 5/8

    You can do that in decimals. Convert both in their decimal forms.
    62% = 0.62
    5/8 = 0.625
    Since 0.625 is greater than 0.62,
    then 62% is less than 5/8
    or 5/8 is greater than 62%.

    ----------------------------------------
    0.9 and 9%

    1) Say, put them in tdecimal forms.
    0.9 = 0.9
    9% = 0.09
    So, since 0.9 is grater than 0.09 ----(0.9 is also 0.90, or 0.9000000, etc)
    then, 0.9 is greater than 9%.

    Or, 9% is less than 0.9

    2) Say, put them in their % forms.
    0.9 = 90%
    9% = 9%
    So, 0.9 is greater than 9%
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  4. #4
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    Hello, Hope!

    Greater than, less than, or equal?

    (1)\;62\%\text{ and }\frac{5}{8}

    (2)\;0.9\text{ and }9\%

    As was pointed out, "percent" means "per hundred".

    To change a percent to a fraction:
    . . write the number over 100,
    . . drop the percent sign.

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    (1)\;\;62\%\text{ and }\frac{5}{8}

    First: . 62\%\:=\:\frac{62}{100}

    Now we compare \frac{62}{100} and \frac{5}{8}
    . . . . \frac{62}{100}\;\;\boxed{?}\;\;\frac{5}{8}


    Here's a trick you can use for comparing fractions: "cross-multiply".

    We have: . \frac{62}{100}\!\begin{array}{cc}_{\nwarrow} \\ ^{\nearrow}\end{array}\!\!\!\!\!\begin{array}{cc}_  {\nearrow} \\ ^{\nwarrow}\end{array}\!\frac{5}{8}\quad\Rightarro  w\quad 62\times8 \;\;\boxed{?}\;\;100 \times 5 . \quad\Rightarrow\quad 496\;\;\boxed{?}\;\;500


    Since 496 < 500, the correct sign is "less than".


    Answer: . 62\%\;<\;\frac{5}{8}

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    (2)\;\;0.9\text{ and }9\%

    First, 9\% = \frac{9}{100}

    We have: . 0.9\;\;\boxed{?}\;\;\frac{9}{100}

    Cross-multiply: . \frac{0.9}{1}\begin{array}{cc}_{\nwarrow} \\ ^{\nearrow}\end{array}\!\!\!\!\begin{array}{cc}_{\  nearrow} \\ ^{\nwarrow}\end{array}\frac{9}{100}\quad\Rightarro  w\quad 0.9 \times 100 \;\;\boxed{?}\;\;1 \times 9\quad\Rightarrow\quad 90\;\;\boxed{?}\;\;9


    Since 90 > 9, the correct sign is "greater than".


    Answer: . 0.9\;> \;9\%

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