Question

Find 9 rational numbers between 0 & 0.1

Answer 1

0 = 0/1*100/100= 0/100
0.1= 1/10*10/10=10/100
rational numbers between them are:- 1/100, 2/100, 3/100, 4/100, 5/100, 6/100, 7/100, 8/100, 9/100.

Answer 2

Answer:

The nine rational numbers that lies between 0 to 0.1 are

$\frac { 1 } { 100 } , \frac { 2 } { 100 } , \frac { 3 } { 100 } , \frac { 4 } { 100 } , \frac { 5 } { 100 } , \frac { 6 } { 100 } , \frac { 7 } { 100 } , \frac { 8 } { 100 } , \frac { 9 } { 100 }$

To Find:  

9 rational numbers between 0 & 0.1

Solution:

Rational Numbers:  

A rational number is a number which is expressed as a fraction or the quotient of two integers.

The rational number consist of numerator (p) and a denominator (q) where, the denominator should not be zero. Some examples of rational numbers are 1/3, 3/100.

Here, the difference between the numbers is given as d.

$\begin{array} { c } { x = 0 , y = 0.1 \text { and } n = 9 } \\\\ { \therefore d = \frac { y - x } { n + 1 } } \end{array}$

$\begin{aligned} d & = \frac { 0.1 - 0 } { 9 + 1 } \\\\ & = \frac { 0.1 } { 10 } \\\\ & = 0.01 \end{aligned}$

Therefore, the required rational numbers that lies between 0 to 0.1 are

$\begin{array} { c } { ( x + d ) ( x + 2 d ) ( x + 3 d ) ( x + 4 d ) ( x + 5 d ) ( x + 6 d ) ( x + 7 d ) ( x + 8 d ) ( x + 9 d ) } \\\\ { = ( 0 + 0.01 ) , ( 0 + 2 \times 0.01 ) , ( 0 + 3 \times 0.01 ) , ( 0 + 4 \times 0.01 ) , ( 0 + 5 \times 0.01 ) , ( 0 + 6 \times 0.01 ) , ( 0 } \\ { + 7 \times 0.01 ) , ( 0 + 8 \times 0.01 ) , ( 0 + 9 \times 0.01 ) } \end{array}$

$\begin{array} { l } { = 0.01 , ( 0 + 0.02 ) , ( 0 + 0.03 ) , ( 0 + 0.04 ) , ( 0 + 0.05 ) , ( 0 + 0.06 ) , ( 0 + 0.07 ) , ( 0 + 0.08 ) , ( 0 } \\ { + 0.09 ) } \end{array}$

$\begin{array} { l } { = 0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09 } \\\\ { = \frac { 1 } { 100 } , \frac { 2 } { 100 } , \frac { 3 } { 100 } , \frac { 4 } { 100 } , \frac { 5 } { 100 } , \frac { 6 } { 100 } , \frac { 7 } { 100 } , \frac { 8 } { 100 } , \frac { 9 } { 100 } } \end{array}$

Therefore, The rational numbers that lies between 0 to 0.1 are

$\frac { 1 } { 100 } , \frac { 2 } { 100 } , \frac { 3 } { 100 } , \frac { 4 } { 100 } , \frac { 5 } { 100 } , \frac { 6 } { 100 } , \frac { 7 } { 100 } , \frac { 8 } { 100 } , \frac { 9 } { 100 }$