# Without Actual Division, Show that Each of the Following Rational Numbers is a Terminating Decimal. Express Each in Decimal Form. (I) 19/3125 - Mathematics

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

(i) 19/3125

#### Solution

19/3125 = 19/5^5 = (19 × 2^5)/(5^5 × 2^5) = 608/100000 = 0.00608
We know either 2 or 5 is not a factor of 19, 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
Is there an error in this question or solution?