Find any five rational numbers between (i)
i
11 and 1
5 ) ) 1
(ii) 0.1 and 0.11 (iii) -1 and -2
Answers
Answer:
: The required numbers are 0.101, 0.102, 0.103, 0.104 and 0.105.
Step-by-step explanation: We are given to find any five rational numbers between 0.1 and 0.11.
We know that
a rational number is of the form \dfrac{p}{q},~q\neq0,
q
p
, q
=0, where p and q are integers.
We have
\begin{gathered}0.1=\dfrac{1}{10}=\dfrac{10}{100}=\dfrac{100}{1000},\\\\\\0.11=\dfrac{11}{100}=\dfrac{110}{1000}.\end{gathered}
0.1=
10
1
=
100
10
=
1000
100
,
0.11=
100
11
=
1000
110
.
Five numbers between 100 and 110 are 101, 102, 103, 104 and 105.
So, the five numbers are
\begin{gathered}\dfrac{101}{1000},\dfrac{102}{1000},\dfrac{103}{1000},\dfrac{104}{1000},\dfrac{105}{1000}\\\\\\\=0.101,0.102,0.103,0.104,0.105.\end{gathered}
Thus, the required numbers are 0.101, 0.102, 0.103, 0.104 and 0.105.