Question

Which of the following statements is false?

(a) Rational numbers have a terminating or non-terminating repeating decimal

form.

(b) Irrational numbers can be written in the form p/q where q is non-zero and both

p, q are integers.

(c) Rational numbers can be written in the form p/q where q is non-zero and both

p, q are integers.

(d) Every number on the number line is either rational or irrational, there’s no third

alternative.​

Answer 1

Answer:

option b is incorrect .

because only rational numbers can be written in the from of p and q

Answer 2

Answer:

(a) True          (b) False           (c) True           (d) True

Step-by-step explanation:

(a) Terminating decimals: If $x=\frac{p}{q}$, then the prime factorisation of $q$ is of the form $2^n5^n$, where $n$ is non-negative integers.

Non-terminating decimal: If $x=\frac{p}{q}$, then the prime factorisation of $q$ is of the form $2^n5^m$, where $n$, $m$ are non-negative integers.

Thus, statement (a) is true.

(b) Irrational numbers are those which can not be written in the $\frac{p}{q}$ form.

Thus, statement (b) is false.

(c) Definition of rational numbers says that the numbers written in the $\frac{p}{q}$ form where $p$, $q$ are integers and $q\neq 0$.

Thus, statement (c) is true.

(d) Since real numbers is the set of rational numbers and irrational numbers.

Also, $N\subset W \subset Z \subset R$.

where $N$ = natural numbers, $W$ = whole numbers, $Z$ = integers and $R$ = real numbers and $N,W,Z$ can be written in $p/q$ form for $q\neq 0$

Thus, statement (d) is true.

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