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29 December, 12:47

Complete the table by converting each decimal to a fraction. Show your work. Repeating decimals. 0.2, 0.5, 0.7

Describe any patterns you noticed when converting the decimals in the table

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  1. 29 December, 13:11
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    Part 1 = 2/9

    Part 2 = 5/9

    Part 3 = 7/9

    Explanation

    To convert the a repeating decimals this are the steps;

    Part 1

    Let x = 0.222222 ... (i)

    10x = 2.222222 ... (ii)

    Subtract equation (i) from equation (ii)

    10x = 2.222222 ...

    -x = 0.222222 ...

    9x = 2.00000 ...

    ∴ 9x = 2

    Divide by 9 both sides;

    x = 2/9

    Part 2

    Let x = 0.5555 ...

    10x = 5.5555 ...

    subtract equation (i) from equation (ii).

    10x = 5.5555 ...

    - x = 0.5555 ...

    9x = 5.0000 ...

    ∴ 9x = 5

    x = 5/9

    Part 3

    Let x = 0.7777 ...

    10x = 7.7777 ...

    Subtracting equation (i) from equation (ii)

    10x = 7.7777 ...

    -x = 0.7777 ...

    9x = 7.000 ...

    ∴ 9x = 7

    x = 7/9

    Pattern noted

    When converting the repeating decimals to fraction only one number was repeating. This made the three decimals have the same fraction.
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