Do five questions to explain how a rational number can be written in p/q form ( take a rational number in non terminating but repeating form
Answers
Step-by-step explanation:
Solution :-
The numbers are in the form of p/q ,where p and q are integers and q≠0 called rational numbers.
1) What is the form of a rational number ?
A ) p/q
Ex :- 2/3 ,-7/9 ....
2) In p/q form ,which of the letters is not equal to zero
A) q ≠0
Ex :-
2/3,-7/9,92
If q = 0 then division with zero is not defined and meaningless
3)What is the decimal form of a rational number ?
A) Every rational number can be expressed as either terminating decimal or non terminating and recurring decimal.
Ex :-
0.5 , 1.77777...
4) How do we write a rational number as a decimal number ?
A) By division
5) Write the the decimals as a rational number?
I) 0.375
Sol : Given number = 0.375
=> 375/1000
=> 15/40
=> 3/8
0.375 = 3/8
ii) 1.7777777....
Sol:- Given number = 1.7777...
Let X = 1.7777...--------(1)
Since the periodicity is 1
We multiply (1) with 10 then
=> 10×X = 1.777...×10
=> 10X = 17.777....-------(2)
(2)-(1)=>
10X = 17.777....
X = 1.777...
(-)
__________
9X = 16.000
_________
=> 9X = 16
=> X = 16/9
1.7777... = 16/9
5) Which letter does represent rational numbers ?
A ) Q
6) Does every number can be expressed as a rational number ?
A) Yes, Every rational number can be written as a rational number
Ex:-
5 = 5/1 = 10/2 = 15/3 =..
0 = 0/1 = 0/10=0/100=...
7) How many rational numbers are there between two numbers ?
A) There are infinitely number of rational numbers. This property is called Densitive Property.
8) How do you find a rational number between two rational numbers ?
A) By Mean method
If a and b are two numbers then the rational number between them is (a+b)/2
Ex :-
The rational number between 3 and 4 is
=> (3+4)/2
=> 7/2
9) which rational.numbers do you represent on the number line?
A) Every rational number can be represented on the number line.
10) Is the non terminating and non recurring decimal a rational number?
A) No ,They are Irrational Numbers.
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