Can you tell me six rational numbers between 3 and 4?

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Kuldeep Guha Mazumder

Mathematics tutor with 6 years of experience

Q (the set of rationals) is dense in R (the set of reals). This means pick any two real numbers and you will find a (and hence infinitely many, since between two real numbers there is always a real number) rational number in between. This guarantees that six rational numbers can be found between 3 and...
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Q (the set of rationals) is dense in R (the set of reals). This means pick any two real numbers and you will find a (and hence infinitely many, since between two real numbers there is always a real number) rational number in between. This guarantees that six rational numbers can be found between 3 and 4. In this case just divide the open interval (3,4) into 7 segments and each of the endpoints of the segments interior to the interval (3,4) is a rational number, viz., (3+1/7)=22/7,(3+2/7)=23/7,(3+3/7)=24/7,(3+4/7)=25/7,(3+5/7)=26/7 and (3+6/7)=27/7. read less
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Govt employee, and having a 10 years of experience as a home tutor

3.14, 3.2, 3.4, 3.5, 3.7 AND 3.8 (OR) 314/100, 32/10, 34/10, 35/10, 37/10 AND 38/10
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Mathematics Trainer

We can write 3=21/7 and 4=28/7 We chose the denominator as 7 as we want to find six rational numbers between 3 & 4. Thus 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are six rational numbers between 3 & 4.
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Math Ninja, Verbal Wizard, Chef and proud to be a geek.

Hi Ashwini, A rational number is a number which can be expressed in the form of a fraction. p/q, where p and q both are rational numbers and q can not be zero. To have any rational number between 3 and 4, you can take the denominator as x and take the numerator any where between 3x and 4x. For example...
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Hi Ashwini, A rational number is a number which can be expressed in the form of a fraction. p/q, where p and q both are rational numbers and q can not be zero. To have any rational number between 3 and 4, you can take the denominator as x and take the numerator any where between 3x and 4x. For example the denominator is 5, then to have the rational number between 3 and 4 you can have the numerator anywhere between 3*5 and 4*5. 16/5, 17/5, 18/5 and 19/5. So six rational numbers between 3 and 4 can be 22/7, 23/7, 24/7, 25/7, 26/7 and 27/7. read less
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Qualified (Engg from NIT) & experienced mentor with 6+ yrs experience.

(3+4)/2; (3+3.5)/2; (3.5+4)/2; (3.75+3.5)/2; (3.75+4)/2; (3+3.25)/2
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Excellence Award Winner ( 7 times )

3.2 3.25 3.45 3.5 3.7 3.75
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3.1 3.2 3.3 3.5 3.9
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Six rational numbers are: 22/7, 23/7, 24/7, 25/7, 26/7 & 27/7.
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Aim Excellence

There are infinite rational nos between any two nos, 3.15, 3.155, 3.1555 , 3.55555 etc, go on, make your own!!
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Quicker Maths

3.1 3.12 3.23 3.45 3.68 3.88 3.98
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