Answer is 1111/900.
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Answers
Step-by-step explanation:
Given :-
1.234 bar on 4
To find :-
Express the given decimal into p/q form ?
Solution :-
Given number = 1.234 ,bar on 4
It can be written as 1.23444...
Let x = 1.23444... -----------(1)
Since , the periodicity is 1,
On multiplying both sides of the equation (1) with 10 then
=> x×10 = 1.23444...×10
=> 10x = 12.344... ---------(2)
Now,
On subtracting (1) from (2) then
=> (2) - (1)
10x = 12.3444...
x = 1.2344...
(-) (-)
_____________
9x = 11.1100...
_____________
=> 9x = 11.11
=> 9x = 1111/100
=> x = (1111/100)/9
=> x = 1111/(100×9)
=> x = 1111/900
Therefore, x = 1111/900
Answer:-
The p/q form of the decimal number 1.234, bar on 4 is 1111/900
Used formulae:-
→ If the periodicity is 1 then multiply the given equation with 10.
Points to know :-
→ The numbers are in the form of p/q, where p and q are integers and q≠0 called Rational numbers.
→ They are denoted by Q
→ Every rational number can be expressed as either terminating decimal or non terminating recurring decimal.
→ In non terminating recurring decimal, the group of digits which are recurring is called its period and the number of digits in the group is called its periodicity.
Ex:-In 2.4444... ,The period = 4, The periodicity = 1