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# TEXTBOOK’S EXERCISE – 1.4

1. Visualise 3.765 on the number line, using successive magnification.
Sol. Step one — The given number lies between 3 and 4.
Step two — Magnify the interval between 3 and 4 and divide it into 10 equal parts.
Step three — The given number lies between 3.7 and 3.8.
Step four — Divide the interval between 3.7 and 3.8 into ten equal parts and magnify it.
Step five — The given number lies between 3.76 and 3.77.
Step six — Magnify the interval between 3.76 and 3.77 and divide it into ten equal parts.
Step seven — 3.675 is the fifth division in this magnification.

Sol. Step one — On the number line the given number 4.26 lies between 4 and 5. (For four decimal places
number is 4.2626.)
Step two — Magnify the interval between 4 and 5 and divide it into 10 equal parts.
Step three — The given number 4.2626 lies between 4.2 and 4.3.
Step four — Magnify the interval between 4.2 and 4.3 and divide it into ten equal parts.

Step five — The given number falls between 4.26 and 4.27.
Step six — Magnify the interval between 4.26 and 4.27 and divide it into ten equal parts.
Step seven — The given number lies between 4.262 and 4.263.
Step eight — Magnify the interval between 4.262 and 4.263 and divide it into ten equal parts.
Step nine — The given number is the sixth division of the given interval.

Class 9 NCERT Solution CHAP 1 NUMBER SYSTEM

#### TEXTBOOK’S EXERCISE – 1.5

1. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π =c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Sol. With a scale or tape, we get only an approximate rational number as the result of our measurement. That is why π can be approximately represented as a quotient of two rational numbers. As a matter of mathematical truth, it is irrational.

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