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    Repeating and Terminating Decimals

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    Please explain how to determine by just looking at a problem if it will be terminating or repeating for example. I need to be able to explain this and answer why?
    If terminating what place value does it terminate in? Why?

    If repeating what is the maximum number of digits in the repeating string it can have? Why?

    A. 0.432
    b. 0.11111...
    c. 0.011111...
    d. 0.010101...
    e. 0.123123123...
    f. 2.2434343...
    g. 0.939339333933339

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    Solution Preview

    Terminating decimals will stop after a certain number of decimal places. They won't have periods after the decimal or bars over the numbers. A and G are terminating. "Terminate" means to finish or end, and these decimals have an ending place.

    Non-terminating decimals don't ever stop. They will have periods after the last number or a bar over some of the numbers. B, C, D, E, and F are non-terminating. "Non-terminating" means they don't have a definite end, ...

    Solution Summary

    This explains the basics of terminating and repeating decimals and includes links for further study.