Question

After how many decimal places the decimal expansion of 51/150 will terminate.

Answer 1

If the factors of denominator of the given rational number is of form 2ⁿ 5^m ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.
SOLUTION:

51/150

= 3×17 / 3× 5 × 2× 5
= 17 / 2¹× 5²
= 17 × 2¹ / 2¹ × 2¹ × 5²
= 34 / 2² × 5²
= 34 / (2×5)²
= 34 / 10²
= 34/100
= 0.34

Hence, it will terminate after 2 places of decimal.

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Answer 2

Answer:

If the factors of denominator of the given rational number is of form 2ⁿ 5^m ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring. Hence, it will terminate after 2 places of decima

Step-by-step explanation: