Number Systems

Exercise 1.4

Visualize \(\begin{align} 3.765\end{align}\) on the number line, using successive magnification.

Steps:

(i) \(3.7\) lies between \(3 \) & \(4\). So we divide the portion between \(3 \) & \(4\). on the number line into \(10\) equal parts

\(3.76\) lies between \(3.7\) and \(3.8\). So, we divide the portion between \(3.7\) and \(3.8\) on the number line into \(10\) equal parts.

\(3.765\) lies between \(3.76\) and \(3.77\) and \(3.77\) .Dividing the line before we got

Visualize \(\begin{align}4 . \overline{26}\end{align}\) on the number line, up to \(4\) decimal places.

\(\begin{align}4 . \overline{26}=4.2626\dots\end{align}\)

(i) \(4.2\) lies between \(4\) &\( 5\). Observe the number line given below

(ii) \(4.26\) lies between \(4.2\) & \(4.3\), shown below on the number line.

(iii) \(4.262\) lies between \(4.26\) & \(4.27\) as shown below.

(iv) \(4.2626\) lies between \(4.262\) & \(4.263\) as shown below

Hence by the successive magnification method required number is obtained in the number line.