Number of Decimal Places in the Decimal Expansion of 33/(2² × 5)

Video Explanation

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Solution

Question: The decimal expansion of the rational number

33 / (2² × 5)

will terminate after:

(a) one decimal place    (b) two decimal places    (c) three decimal places    (d) more than 3 decimal places

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

Denominator = 2² × 5¹

Step 2: Use the Rule for Terminating Decimal Expansion

If a rational number in its lowest form has denominator of the form 2^m × 5ⁿ, then its 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 two decimal places.

✔ Correct option: (b) two decimal places

Conclusion

Thus, the rational number 33/(2² × 5) has a terminating decimal expansion after two decimal places.