Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{13}{3125}$ [1 MARK]

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Solution

Concept : 0.5 Mark
Application : 0.5 Mark

$3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^{5}$

$\Rightarrow$ Denominator is of the form $2^{n} {.5}^{m}$ , where m=5 and n=0.

It means rational number $\frac{13}{3125}$ has a terminating decimal expansion.

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

Q. Without actually performing the long division method, state whether the following rational numbers will have a terminating decimal expansion or a non -terminating repeating decimal expansion.

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 133125 [1 MARK]

Concept : 0.5 Mark Application : 0.5 Mark 3125=5×5×5×5×5=55 ⇒ Denominator is of the form 2n.5m, where m=5 and n=0. It means rational number 133125 has a terminating decimal expansion.

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{13}{3125}$ [1 MARK]

Concept : 0.5 Mark
Application : 0.5 Mark

$3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^{5}$

$\Rightarrow$ Denominator is of the form $2^{n} {.5}^{m}$ , where m=5 and n=0.

It means rational number $\frac{13}{3125}$ has a terminating decimal expansion.