Question

Visualize $2.665$ on the number line, using successive magnification.

Answer 1

We know that $2.665$ lies between $2$ and $3$. So, we divide the number line into $10$ equal parts and mark each point of division. The first mark on the right of $2$ will be $2.1$ followed by $2.2$ and so on till the point left of $3$ which will be $2.9$.

Now, the magnified view of this will show that $2.665$ lies between $2.6$ and $2.7$. So, our focus will be now $2.6$ and $2.7$.

We divide this again into $10$ equal parts. The first part will be $2.61$ followed by $2.62$ and so on.

Now, we now magnify this again and find that $2.665$ lies between $2.66$ and $2.67$. So, we magnify this portion and divide it again into $10$ equal parts. The first part will represent $2.661$, next will be $2.662$ and so on.

Hence, 5th mark in this subdivision as shown in the figure is $2.665$.