need answer to both parts please
Answers
Step-by-step explanation:
Solution :-
General method :-
Given numbers are 1.3 bar and 1.4 bar
1.3 bar = 1.333...
1.4 bar = 1.444...
Two rational numbers between them
= 1.3222... and 1.43333...
Mean Method :-
Let X = 1.333...------------(1)
since the periodicity is 1 then multiply (1) with 10
=> 10×X = 1.333...×10
=>10X = 13.333...--------(2)
(2)-(1)
10X = 13.333...
X = 1.333...
(-)
____________
9X = 12.000...
____________
=> 9X = 12
=> X = 12/9
=> X = 4/3
and
Let X = 1.444...------------(1)
since the periodicity is 1 then multiply (1) with 10
=> 10×X = 1.444...×10
=>10X = 14.444...--------(2)
(2)-(1)
10X = 14.444...
X = 1.444...
(-)
____________
9X = 13.000...
____________
=> 9X = 13
=> X = 13/9
Now we have 12/9 and 13/9
The rational number between them by mean method (a+b)/2
=> [(12/9)+(13/9)]/2
=> (25/9)/2
=> 25/18
and Second rational number
=>[(12/9)+(25/18)]/2
=> [(24+25)/18]/2
=> (49/18)/2
=> 49/36
The two rational numbers between them are 25/18 and 49/36
ii)General method :-
Given numbers are 2.23 bar and 2.24 bar
2.23 bar = 2.232323...
2.24 bar = 2.242424...
Two rational numbers between them
= 2.232525... and 2.239899...
Mean Method :-
Let X = 2.232323...------------(1)
since the periodicity is 2 then multiply (1) with 100
=> 100×X = 2.232323...×100
=>100X = 223.232323...--------(2)
(2)-(1)
100X = 223.232323...
X = 2.232323...
(-)
__________________
99X = 221.000000...
__________________
=> 99X = 221
=> X = 221/99
and
Let X = 2.242424...------------(1)
since the periodicity is 2 then multiply (1) with 100
=> 100×X = 2.242424...×10
=>100X = 224.242424...--------(2)
(2)-(1)
100X = 224.242424...
X = 2.242424...
(-)
_________________
99X = 222.000000
_________________
=> 92X = 222
=> X = 222/99
Now we have 221/99 and 222/99
The rational number between them by mean method (a+b)/2
=> [(221/99)+(222/99)]/2
=> (443/99)/2
=> 443/198
and Second rational number
=>[(221/99)+(443/198)]/2
=> [(442+443)/198]/2
=> (885/198)/2
=> 885/396
The two rational numbers between them are 443/198 and 885/396
Used formulae:-
.Mean Method :-
The rational number between the two numbers a and b is (a+b)/2