10. Please help please someone ASAP I need this please
Answers
Answer:
please help me if you know physics please
Step-by-step explanation:
10) Given :-
0.54545454... + 0.22222...
To find :-
Convert into p/q form ?
Solution :-
Given that :
0.54545454... + 0.22222...
On taking 0.54545454...
Let X = 0.545454...-------------(1)
Since the periodicity is 2 then multiply (1) with 100 then
=> X×100 = 0.545454...×100
=> 100X = 54.545454...-------------(2)
On Subtracting (1) from (2)
100X = 54.545454...
X = 0.545454...
(-) (-)
___________________
99X = 54.000000...
___________________
=> 99X = 54
=> X = 54/99
=> X = 6/11
On taking 0.2222...
Let X = 0.2222...-------------(1)
Since the periodicity is 1 then multiply (1) with 10 then
=> X×10 = 0.2222...×10
=> 10X = 2.222...-------------(2)
On Subtracting (1) from (2)
10X = 2.222...
X = 0.222...
(-) (-)
___________________
9X = 2.000...
___________________
=> 9X = 2
=> X = 2/9
Now,
We have ,0.54545454... + 0.22222...
=> (6/11)+(2/9)
LCM of 11 and 9 is 99
=> [(6×9)+(2×11)]/99
=> (54+22)/99
=> 76/99
Therefore, 0.54545454... + 0.22222... = 76/99
Answer:-
The p/q form of the given expression is 76/99
Used formulae :-
- If the periodicity is 1 then multiply the equation with 10.
- If the periodicity is 2 then multiply the equation with 100
Points to know:-
The number of recurring digits after the decimal point in a non terminating and recurring decimal is called the Periodicity.