Question 4 - End-of-Chapter Exercises - Chapter 3 Class 9 - The World of Numbers (Ganita Manjari I)

Transcript

Question 4 (i) Locate the following rational numbers on the number line. (i) 0.532 To plot 0.532, we just magnify our number line step-by-step Using successive magnification Zoom 1 (Tenths): 0.532 lies between 0 and 1. We zoom into that space and divide it into 10 parts. Our number lies right between 0.5 and 0.6. Zoom 2 (Hundredths): We take the tiny segment between 0.5 and 0.6 and magnify it, dividing it into 10 smaller parts. 0.532 lies between 0.53 and 0.54. Zoom 3 (Thousandths): Finally, we magnify the space between 0.53 and 0.54. We count two ticks over to accurately plot our point at exactly 0.532. Question 4 (ii) Locate the following rational numbers on the number line. (ii) 1.15 ̅ Now, 1.15 ̅ = 1.1555…. Let’s plot the number line Using successive magnification Zoom 1 (Tenths): It lies between 1 and 2. We zoom in to find it lies between 1.1 and 1.2. Zoom 2 (Hundredths): We magnify the space between 1.1 and 1.2. Because the next digit is 5, it lies between 1.15 and 1.16. Zoom 3 (Thousandths): We magnify the space between 1.15 and 1.16. Because the repeating digit is 5, it lies between 1.155 and 1.156. Note: Because this decimal is non-terminating, you can never place an exact, final dot. You just keep zooming in infinitely! To plot it practically, you place a dot slightly past the halfway mark of whatever your deepest magnification level is.