Question

# Visualise the representation of $5.3\overline{7}$ on the number line upto 5 decimal places, that is upto 5.37777.

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Solution

## We know that $5.3\overline{7}$ will lie between 5 and 6. So, we locate $5.3\overline{7}$ between 5 and 6. We divide this portion of the number line between 5 and 6 into 10 equal parts and use a magnifying glass to visualize $5.3\overline{7}$ . $5.3\overline{7}$ lies between 5.37 and 5.38. To visualize $5.3\overline{7}$ more accurately we use a magnifying glass to visualize between 5.377 and 5.378. Again, we divide the portion between 5.377 and 5.378 into 10 equal parts and visualize more closely to represent $5.3\overline{7}$ as given in the figure. This is located between 5.3778 and 5.3777.

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