Question

what is meant by terminating decimal

Answer 1

HEY MATE HERE IS YOUR ANSWER

Terminating and Repeating Decimals. Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . If you end up with a remainder of , then you have a terminating decimal.

A decimal number is a representation of some real number using digits [math]a_i \in \{0,1,2,3,4,5,6,7,8,9\}[/math] with place-value notation. That is, it can be written in the form

[math]\sum_{i = 0}^n a_i 10^{m-i},[/math]

where [math]m \in \mathbb{Z}[/math], and we allow the possibility that the limit as [math]n \to \infty[/math] may be taken.

A terminating decimal is one where [math]n[/math] is strictly finite, or, equivalently, where [math]n = \infty[/math] and there is some finite [math]k[/math] such that every [math]a_i = 0[/math] for [math]i > k[/math]. This implies that the number thus represented is a rational number of the form [math]\tfrac{p}{q}[/math], where [math]q = 2^{k_1}5^{k_2}[/math], for non-negative [math]k_1, k_2[/math].

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Answer 2

When a fraction is p/q, where q can be written in the form of 2^n x 5^m then it is called terminating decimal