write whether the rational no. 51 divided by 1500 will have terminating decimal expansion or a non-terminating decimal expansion .how?

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Solution

$\frac{51}{1500} = \frac{3 \times 17}{2 \times 2 \times 5 \times 5 \times 5 \times 3} = \frac{17}{2 \times 2 \times 5 \times 5 \times 5} = \frac{17}{2^{2} \times 5^{3}}$
Here we can see the denominator can be written in the form of $2^{m} \times 5^{n}$ . Therefore its terminating expansion.

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write whether the rational no. 51 divided by 1500 will have terminating decimal expansion or a non-terminating decimal expansion .how?

511500 = 3×172×2×5×5×5×3 = 172×2×5×5×5 = 1722×53 Here we can see the denominator can be written in the form of 2m×5n. Therefore its terminating expansion.

$\frac{51}{1500} = \frac{3 \times 17}{2 \times 2 \times 5 \times 5 \times 5 \times 3} = \frac{17}{2 \times 2 \times 5 \times 5 \times 5} = \frac{17}{2^{2} \times 5^{3}}$
Here we can see the denominator can be written in the form of $2^{m} \times 5^{n}$ . Therefore its terminating expansion.