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 $5.37777$.
Once again we proceed by successive magnification, and successively decrease the lengths of the portions of the number line in which $5.3 \overline{7}$ is located. First, we see that $5.3 \overline{7}$ is located between $5$ and $6 .$ In the next step, we locate $5.3 \overline{7}$ between $5.3$ and $5.4 .$ To get a more accurate visualization of the representation, we divide this portion of the number line into $10$ equal parts and use a magnifying glass to visualize that $5.3 \overline{7}$ lies between $5.3 \overline{7}$ and $5.38 .$ To visualize $5.3 \overline{7}$ more accurately, we again divide the portion between $5.3 \overline{7}$ and 5.38 into ten equal parts and use a magnifying glass to visualize that $5.3 \overline{7}$ lies between $5.377$ and $5.378 .$ Now to visualize $5.3 \overline{7}$ still more accurately, we divide the portion between $5.377 $ an $5.378$ into $10$ equal parts, and visualize the representation of $5.3 \overline{7}$ as in Fig. $(iv)$. Notice that $5.3 \overline{7}$ is located closer to $5.3778$ than to $5.3777$ [see Fig $(iv)$].
Similar Questions
Write the following in decimal form and say what kind of decimal expansion each has :
$(i)$ $\frac{36}{100}$
$(ii)$ $\frac{1}{11}$
$(iii)$ $4 \frac{1}{8}$
$(iv)$ $\frac{3}{13}$
$(v)$ $\frac{2}{11}$
$(vi)$ $\frac{329}{400}$
Write the following in decimal form and say what kind of decimal expansion each has :
$(i)$ $\frac{36}{100}$
$(ii)$ $\frac{1}{11}$
$(iii)$ $4 \frac{1}{8}$
$(iv)$ $\frac{3}{13}$
$(v)$ $\frac{2}{11}$
$(vi)$ $\frac{329}{400}$
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 $q \neq 0$.
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.
Show that $1.272727 \ldots=1 . \overline{27}$ . can be expressed in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Show that $1.272727 \ldots=1 . \overline{27}$ . can be expressed in the form $\frac {p }{q }$, where $p$ and $q$ are integers and $q \ne 0$.
Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$
Express the following in the form $\frac {p}{q}$, where $p$ and $q$ are integers and $q \ne 0$.
$(i)$ $0 . \overline{6}$
$(ii)$ $0 . 4\overline{7}$
$(iii)$ $0 . \overline{001}$