Visualise \(5.3\overline{7}\) on the Number Line upto 5 Decimal Places
Diagram (Successive Magnification)
Construction Method:
Step 1:
Mark 5 and 6 on the number line.
\[ 5 < 5.3777 < 6 \]
Step 2:
Divide [5, 6] into 10 equal parts and locate 5.3.
Step 3:
Zoom into [5.3, 5.4] and locate 5.37.
Step 4:
Zoom into [5.37, 5.38] and locate 5.377.
Step 5:
Zoom into [5.377, 5.378] and locate 5.3777.
Final Result:
The number \(5.3\overline{7}\) is visualised upto 5 decimal places as: \[ 5.3777 \]
Concept Used:
Successive magnification helps locate repeating decimals by zooming into smaller intervals step-by-step.