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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) `151/600` - 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) `151/600`

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Solution

`15/1600 = 15/(2^6 × 5^2) = (15 × 5^4)/(2^6 × 5^6) = 9375/1000000 = 0.009375`
We know either 2 or 5 is not a factor of 15, 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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