Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{64}{455}$ [1 MARK]

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Solution

Concept : 0.5 Mark
Application : 0.5 Mark

The prime factors of 455 are

$455 = 5 \times 91$

Therefore, denominator is not of the form $2^{n} {.5}^{m}$ , where m and n are non-negative integers.

It means rational number $\frac{64}{455}$ has 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 : 64455 [1 MARK]

Concept : 0.5 Mark Application : 0.5 Mark The prime factors of 455 are 455=5×91 Therefore, denominator is not of the form 2n.5m, where m and n are non-negative integers. It means rational number 64455 has a non-terminating repeating 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 : $\frac{64}{455}$ [1 MARK]

Concept : 0.5 Mark
Application : 0.5 Mark

The prime factors of 455 are

$455 = 5 \times 91$

Therefore, denominator is not of the form $2^{n} {.5}^{m}$ , where m and n are non-negative integers.

It means rational number $\frac{64}{455}$ has a non-terminating repeating decimal expansion.