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Number Systems

Short Answer Type

1. Is zero a rational number? Can you write it in the form

straight p over straight q comma

where p and q are integers and q ≠ 0?

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2. Find six rational numbers between 3 and 4.

There can be infinitely many rational numbers between 3 and 4.

fraction numerator 3 plus 4 over denominator 2 end fraction equals 7 over 2 fraction numerator 3 plus begin display style 7 over 2 end style over denominator 2 end fraction equals 13 over 4 fraction numerator 3 plus begin display style 13 over 4 end style over denominator 2 end fraction equals 25 over 8 fraction numerator 3 plus begin display style 25 over 8 end style over denominator 2 end fraction equals 49 over 16 fraction numerator 3 plus begin display style 49 over 16 end style over denominator 2 end fraction equals 97 over 32 fraction numerator 3 plus begin display style 97 over 32 end style over denominator 2 end fraction equals 193 over 64

Thus, six ratonal numbers between 3 and 4 are

7 over 2 comma space 13 over 4 comma space 25 over 8 comma space 49 over 16 comma space 97 over 32 space and space 193 over 64

.

Alter

open table attributes columnalign right end attributes row cell 3 equals 3 over 1 equals fraction numerator 3 cross times 7 over denominator 3 cross times 7 end fraction equals 21 over 7 end cell row cell 4 equals 4 over 1 equals fraction numerator 4 cross times 7 over denominator 4 cross times 7 end fraction equals 28 over 7 end cell end table close curly brackets space 6 plus 1 equals 7

Thus, six rational numbers between 3 and 4 can be taken as

22 over 7 comma space 23 over 7 comma space 24 over 7 comma space 25 over 7 comma space fraction numerator 26 over denominator space 7 end fraction space and space 27 over 7.

Note. This is known as the method of finding rational numbers in one step.

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3. Find five rational numbers between

3 over 5 space and space space 4 over 5.

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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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Find four rational numbers be-tween $3 over 7 space a n d space 5 over 7$

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6. Find four rational numbers be-tween

1 third space a n d space 4 over 5.

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7. Find three rational numbers between 0 and 0.1. Also, find twenty rational numbers between 0 and 0.1.

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Insert three rational numbers between $negative 2 over 5 space and space minus 1 fifth$

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9. Find three rational numbers

2 over 5 space and space space 7 over 8

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10.

Are the following statements true or false? Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.

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