Classify the following numbers as rational or irrational :
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$
Classify the following numbers as rational or irrational :
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$
$(i)$ $\sqrt{23}=4.79583152331 \ldots$
As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.
$(ii)$ $\sqrt{225}=15=\frac{15}{1}$
It is a rational number as it can be represented in $\frac {p}{q}$ form.
$(iii)$ $0.3796$
As the decimal expansion of this number is terminating, therefore, it is a rational number.
$(iv)$ $7.478478 \ldots$ $=7 . \overline{478}$
As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.
$(v)$ $1.101001000100001 \ldots$
As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.
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State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number
Are the following statements true or false ? Give reasons for your answers.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.
Are the following statements true or false ? Give reasons for your answers.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.