Number Systems
Exercise 1.4
Visualize \(\begin{align} 3.765\end{align}\) on the number line, using successive magnification.
Solution Video Solution
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.