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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) `24/125` - 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) `24/125`

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Solution

`24/125 = 24/5^3 =( 24 × 2^3)/(5^3 × 2^3) = 192/1000 = 0.192`
We know 5 is not a factor of 23, 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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