Number of Decimal Places in the Decimal Expansion of 14587/1250

Video Explanation

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Solution

Question: The decimal expansion of the rational number

14587 / 1250

will terminate after:

(a) one decimal place    (b) two decimal place    (c) three decimal place    (d) four decimal place

Step 1: Prime Factorisation of the Denominator

1250 = 125 × 10

125 = 5³,   10 = 2 × 5

∴ 1250 = 2 × 5⁴

Step 2: Use the Rule for Terminating Decimals

If the denominator (in lowest form) is of the form 2^m × 5ⁿ, then the decimal expansion terminates after max(m, n) decimal places.

Here, m = 1 and n = 4

max(1, 4) = 4

Final Answer

✔ The decimal expansion terminates after 4 decimal places.

✔ Correct option: (d) four decimal place

Conclusion

Thus, the rational number 14587/1250 has a terminating decimal expansion after 4 decimal places.