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Without Actual Division, Show that Each of the Following Rational Numbers is a Terminating Decimal. Express Each in Decimal Form. (I) `17 /320` - Mathematics

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Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.

(i) `17 /320`

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Solution

`17/320 = 17/(2^6 × 5) = (17 × 5^5)/(2^6 × 5^6) = 53125/1000000 = 0.053125`
We know either 2 or 5 is not a factor of 17, so it is in its simplest form.
Moreover, it is in the form of (2m × 5n). 
Hence, the given rational is terminating.

Concept: Euclid’s Division Lemma
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