Chapter 01 Number Systems Exercise-01
EXERCISE 1.1
1. Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$ ?
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Solution
Yes. Zero is a rational number as it can be represented as $\frac{0}{1}$ or $\frac{0}{2}$ or $\frac{0}{3}$ etc.
2. Find six rational numbers between 3 and 4 .
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Solution
There are infinite rational numbers in between 3 and 4 .
3 and 4 can be represented as respectively.
Therefore, rational numbers between 3 and 4 are $\frac{25}{8}, \frac{26}{8}, \frac{27}{8}, \frac{28}{8}, \frac{29}{8}, \frac{30}{8}$
3. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
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Solution
numbers
$\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$
$ \frac{3}{5} \text{ and } \frac{4}{5} $
$\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}$
numbers between $\frac{3}{5}$ and $\frac{4}{5}$
4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
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Solution
(i) True; since the collection of whole numbers contains all natural numbers.
(ii) False; as integers may be negative but whole numbers are positive. For example: -3 is an integer but not a whole number.
(iii) False; as rational numbers may be fractional but whole numbers may not be. For example: $\frac{1}{5}$ is a rational number but not a whole number.
