Insert 16 rational numbers between 2.1 and 2.2.
Answers
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
2101
,
1000
2102
,
1000
2103
,
1000
2104
,
1000
2105
,
1000
2106
,
1000
2107
,
1000
2108
,
1000
2109
,
1000
2110
,
1000
2111
,
1000
2112
,
1000
2113
,
1000
2114
,
1000
2115
,
1000
2116
Answer:
heyy!!
let
2.1=2.100
&
2.2=2.200
now 16 no. are : 2.110,2.120,2.121,2.122,2.123,2.124,2.125,2.126,2.130,2.140,2.150,2.160,2.170,2.180,2.190,2.200
hope it helps u