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    The decimal expansion of 31/2.5 will terminate after:
    Question

    The decimal expansion of 31/2.5 will terminate after:

    A.

    two decimal places

    B.

    one decimal place

    C.

    more than three decimal places

    D.

    three decimal places

    Correct option is B

    Solution:

    Rewrite the denominator in fractional form:
    312.5=3152\frac{31}{2.5} = \frac{31}{\frac{5}{2}}​​

    Simplify by multiplying the numerator and the denominator by 2 to eliminate the decimal:
    31×252×2=625\frac{31 \times 2}{\frac{5}{2} \times 2} = \frac{62}{5}​​

    Now, divide to find the decimal expansion:
    625=12.4\frac{62}{5} = 12.4​​

    Since the decimal expansion 12.4 terminates after one decimal place, the correct answer is:
    The decimal expansion of  312.5\frac{31}{2.5}​ will terminate after one decimal place. Thus, the correct option is B.

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