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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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