Find a rational number that is between 9.5 and 9.7. Explain why it is rational.
Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.
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Answers
Answer:
9.6 is a rational no. Between 9.5 and 9.7.
9.647746.........is a irrational no. between 9.5&9.6
Step-by-step explanation:
As 9.6=96/10
&
9.64776........ can't be expressed in p/q form.
Given : 9.5 and 9.7
To Find : An irrational number that is between 9.5 and 9.7.
the decimal approximation of the irrational number to the nearest hundredth
Solution:
Rational numbers are real numbers which can be expresses in the form
p/q where p and q are integers and q ≠ 0
All real numbers which are not rational are irrational.
9.5 = 95/10
9.7 = 97/10
95/10 < x < 97/10
=> 95²/100 < x² < 97²/100
95² = 9025
97² = 9409
9025 < 9100 , 9200 , 9300 , 9400 < 9409
95²/100 < 9100/100 < 97²/100
x² = 9100/100 = 91
=> x= √91
or = x = √92 , √93 and √94 are few more
√91 is an irrational number that is between 9.5 and 9.7.
This can not be represented at p/q form hence not rational so irrational
There exist infinite rational number between any two different rational or irrational numbers.
√91 ≈ 9.539
≈ 9.54
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