A number whose decimal expansion is terminating or non-terminating recurring is called a ___ number.

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Solution

Terminating decimal numbers:
The numbers which have finite numbers after the decimal point are called terminating decimal numbers.
Non-terminating recurring decimal numbers:
The numbers which continue endlessly and have repeating numbers after the decimal point are called non-terminating recurring decimal numbers.
Explanation:
A rational number can be written in the form $\frac{p}{q}$ where $p, q$ are integers and coprime and $q$ ≠ $0 .$
Consider the number $33.33333 \dots \dots .$
It is a rational number as it can be represented in the form of $\frac{100}{3} .$
It is a non-terminating repeating decimal number.
Let us consider another number $0.5 .$
It is a rational number as it can be represented in the form of $\frac{1}{2} .$
It is a terminating decimal number.
Hence, a number whose decimal expansion is terminating or non-terminating recurring is called a rational number.

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Similar questions

Q. Decimal expansion of a rational number cannot be
(a) non-terminating
(b) non-terminating and recurring
(c) terminating
(d) non-terminating and non-recurring

Q. Decimal expansion of

\sqrt{2}

is
(a) a finite decimal
(b) 1.4121
(c) non-terminating recurring
(d) non-terminating, non-recurring

The decimal expansion of $\sqrt{2}$ is

(a) finite decimal

(b) 1.4121

(d) non terminating, non recurring

Consider the following three statements.
Statement–1: A number whose decimal expansion is terminating is a rational number.
Statement–2: A number whose decimal expansion is non– terminating recurring is a rational number.
Statement–3: A number whose decimal expansion is terminating non recurring is irrational number.
Which of the following is true?

Q. Question 5
The decimal expansion of the number

\sqrt{2}

is

A) A finite decimal
B) 1.41421
C) Non-terminating recurring
D) Non-terminating non-recurring.

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