Question

insert 16 rational number between 2.1 and 2.2​

Answer 1

Answer:

Given rational nos are 2.1 and 2.2

To find: 16 rational nos between them

First we find their Equivalent rational nos. such that there exist 16 or more than 16 rational no between them.

Consider,

2.1\:\:\:and\:\:\:2.22.1and2.2

⇒ \frac{21}{10}\:\:\:and\:\:\:\frac{22}{10}

10

21

and

10

22

⇒ \frac{21}{10}\times\frac{100}{100}\:\:\:and\:\:\:\frac{22}{10}\times\frac{100}{100}

10

21

×

100

100

and

10

22

×

100

100

⇒ \frac{2100}{1000}\:\:\:and\:\:\:\frac{2200}{1000}

1000

2100

and

1000

2200

Now there exist 100 rational nos between them

16 from them are the following,

\implies\frac{2101}{1000}\:,\:\frac{2102}{1000}\:,\:\frac{2103}{1000}\:,\:\frac{2104}{1000}\:,\:\frac{2105}{1000}\:,\:\frac{2106}{1000}\:,\:\frac{2107}{1000}\:,\:\frac{2108}{1000}\:,\:\frac{2109}{1000}\:,\:\frac{2110}{1000}\:,\:\frac{2111}{1000}\:,\:\frac{2112}{1000}\:,\:\frac{2113}{1000}\:,\:\frac{2114}{1000}\:,\:\frac{2115}{1000}\:,\:\frac{2116}{1000}⟹

1000