find a rational number between the two irrational number a= 3.64279....and b=3.65327
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daneenthecool
daneenthecool
22.06.2019
Math
Secondary School
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5. Find a rational number between the two irra.
tional numbers a = 3.64279... and b = 3.65327....
with full explanation please
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Muntazirali
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Question⇒ 5. Find a rational number between the two irra.
tional numbers a = 3.64279... and b = 3.65327....
Step-by-step explanation:
There are infinite rational numbers between these two - and finding a rational between them is easy - since they are both rational themselves :
3.64279 = \frac{364279}{100,000} and 3.65327 = \frac{364327}{100,000}
So - even with a denominator of 100,000, then there are
364327 - 364279 = 48 rationals :
\frac{364280}{100,000}
\frac{364281}{100,000}
\frac{364282}{100,000}
…
\frac{364327}{100,000}
As you can see - you could increase the denominator to 1,000,000 and you can have another nearly 500 rationals, and increase the denominator again, and again, and again - in-fact you can make the denominator as big as you like, and there will always be rationals to find and no limit to how big the denominator can get.