Number of Decimal Places in the Decimal Expansion of 23/(2² × 5)

Video Explanation

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Solution

Question: The number of decimal places after which the decimal expansion of the rational number

23 / (2² × 5)

will terminate, is:

(a) 1    (b) 2    (c) 3    (d) 4

Step 1: Write the Denominator in the Form 2^m × 5ⁿ

Denominator = 2² × 5¹

Step 2: Use the Rule for Terminating Decimals

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

Step 3: Find the Number of Decimal Places

m = 2, n = 1

max(2, 1) = 2

Final Answer

✔ The decimal expansion terminates after 2 decimal places.

✔ Correct option: (b) 2

Conclusion

Thus, the rational number 23/(2² × 5) has a terminating decimal expansion after 2 decimal places.