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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) `171/800` - 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) `171/800`

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Solution

`171/800 = 171/(2^5 × 5^2 )= (171 × 5^3)/(2^5 × 5^5) = 21375/100000 = 0.21375`
We know either 2 or 5 is not a factor of 171, 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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