Question

Insert 100 rational numbers between -3/13 and 9/13 ?

Answer 1

Answer:

Any 100 numbers between the values -3/13 and 9/13 is the answers. The numbers be $- \frac { 299 } { 1300 } , - \frac { 298 } { 1300 } , - \frac { 297 } { 1300 } , - \frac { 296 } { 1300 } , \ldots$

Solution:

Given the values are  

$- \frac { 3 } { 13 } \text { and } \frac { 9 } { 13 }$

To insert “100 rational numbers between” $- \frac { 3 } { 13 } \text { and } \frac { 9 } { 13 }$

Let us multiply and divide the terms by 100,

$\begin{aligned} - \frac { 3 } { 13 } & = - \frac { 3 \times 100 } { 13 \times 100 } \\\\ = & - \frac { 300 } { 1300 } \\\\ \frac { 9 } { 13 } & = \frac { 9 \times 100 } { 13 \times 100 } \\\\ & = \frac { 900 } { 1300 } \end{aligned}$

∴ “100 rational numbers between”  $- \frac { 3 } { 13 } \text { and } \frac { 9 } { 13 } = 100 \text { numbers between } - \frac { 300 } { 1300 } \text { and } \frac { 900 } { 1300 }$

Any 100 rational numbers between $- \frac { 300 } { 1300 } \text { and } \frac { 900 } { 1300 } \text { is } - \frac { 299 } { 1300 } , - \frac { 298 } { 1300 } , - \frac { 297 } { 1300 } , - \frac { 296 } { 1300 } , \ldots$  

Answer 2

Answer:

$100\: rational\: numbers\\ \: between \: \frac{-3}{13} \: and \: \frac{9}{13} \\\: are \: \frac{-302}{1313},\frac{-301}{1313},\frac{-300}{1313},\\\frac{-299}{1313},...,\frac{-201}{1313}$

Step-by-step explanation:

$Since\: we \:want \\\:100\: numbers ,\\\: we \:write \:\frac{-3}{13} \: and \: \frac{9}{13}\\ \: as \: rational \: numbers\\ \: with \: denominator\: \\100+1 = 101$

$\frac{-3}{13}\\=\frac{-3\times 101}{13\times 101}\\=\frac{-303}{1313}--(1)$

$\frac{9}{13}\\=\frac{9\times 101}{13\times 101}\\=\frac{909}{1313}--(2)$

Therefore,

$100\: rational\: numbers\\ \: between \: \frac{-3}{13} \: and \: \frac{9}{13} \\\: are \: \frac{-302}{1313},\frac{-301}{1313},\frac{-300}{1313},\\\frac{-299}{1313},...,\frac{-201}{1313}$

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