Express $0.99999 \ldots$ in the form $\frac{p}{q}$. Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense.
Express $0.99999 \ldots$ in the form $\frac{p}{q}$. Are you surprised by your answer ? With your teacher and classmates discuss why the answer makes sense.
Let $x=0.9999 \ldots$
Multiply both sides by $10,$ we have $[\because$ There is only one repeating digit.]
$10 \times x =10 \times(0.99999 \ldots)$
or $10 x=9.9999 \ldots$
Subtracting $(1)$ from $(2)$, we get
$10 x-x=(9.9999 \ldots)-(0.9999 \ldots)$
or $9 x=9$
or $x=\frac{9}{9}=1$
Thus, $\quad 0.9999 \ldots=1$
As $0.9999 \ldots$ goes on forever, there is no gap between $1$ and $0.9999 \ldots$
Hence both are equal.
Similar Questions
Divide $8 \sqrt{15}$ by $2 \sqrt{3}$
Divide $8 \sqrt{15}$ by $2 \sqrt{3}$
Show that $0.2353535 \ldots=0.2 \overline{35}$ can be expressed in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.
Show that $0.2353535 \ldots=0.2 \overline{35}$ can be expressed in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.
Visualize the representation of $5.3 \overline{7}$. on the number line upto $5$ decimal places, that is, up to $5.37777$.
Visualize the representation of $5.3 \overline{7}$. on the number line upto $5$ decimal places, that is, up to $5.37777$.
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
Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.