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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) `23/(2^3 × 5^2)` - 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) `23/(2^3 × 5^2)`

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Solution

`23/(2^3 × 5^2) = (23 × 5)/(2^3 × 5^3) = 115/1000 = 0.115`
We know either 2 or 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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