Question

Please solve ques no. 2 ​

Answer 1

QuestioN :

2. Find the two integers between which the given rational numbers lie. Also, find their actual position on a number line.

• a) 15 / 17.
• b) 12 / 5.
• c) - 34 / 16.
• d) - 12 / 70.

SolutioN :

✎ We have, Rational number.

• Rational number can be define as a number which can Express in the form of p / q, where q ≠ 0.

✎ Rational number :

• 15 / 17.
• 12 / 5.
• - 34 / 16.
• - 12 / 70.

$\rule{140}2$

✎ Let's Taking Some Cases, to find greatest integer and least integer.

• Out of four given Rational number,
• The least rational number is - 34 / 16.
• The greatest rational number is 12 / 5.

$\rule{200}2$

☛ Case 1.

• For greatest possible integer.

$\tt \mapsto \dfrac{ - 34}{16}$

$\tt \mapsto - 2.125$

✵ Integer form - 3.

$\rule{200}2$

☛ Case 2.

• For least possible integer.

$\tt \mapsto \dfrac{ 12}{5}$

$\tt \mapsto 2.4$

✵ Integer form 3.

$\rule{200}2$

${\tt{Note:}}\begin{cases} \sf{The \: least \: possible \: integer} \\ \sf{come \: after \: greater \: rational} \\ \sf{number.}\end{cases}$

$\tt{Note:}\begin{cases} \sf{The \: greater \: possible \: integer} \\ \sf{come \: after \: least \: rational} \\ \sf{number.}\end{cases}$

♢ Given, four rational lies on number line between - 3 , 3.

$\setlength{\unitlength}{1cm}\thicklines\begin{picture}(0,0)\put(3,3){\line(1,0){6}}\put(3,3){\circle*{0.2}}\put(2.6,3.5){ -3 } \put(4,3){\circle*{0.2}}\put(3.6,3.5){ \tt{\dfrac{-34}{16}} } \put(5,3){\circle*{0.2}}\put(4.6,3.5){ \tt{\dfrac{-12}{70}} } \put(6,3){\circle*{0.2}}\put(5.9,3.5){ 0 } \put(7,3){\circle*{0.2}}\put(6.9,3.5){ \tt{\dfrac{15}{17}} }\put(8,3){\circle*{0.2}}\put(9,3){\circle*{0.2}}\put(7.9,3.5){ \tt{\dfrac{12}{5}} }\put(8.9,3.5){ 3 }\end{picture}$