Question
Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}.$
✓
Answer
$\frac{5}{7}=0.\overline{714285}$$\frac{9}{11}=0.\overline{81}$
3 irrational numbers are-
0.73073007300073000073... 0.75075007500075000075... 0.790790079000790000...
Concept Insight: There is infinite number of rational and irrational numbers between any two rational numbers. Convert the number into its decimal form to find irrationals between them.
Alternatively following result can be used to answer:
Irrational number between two numbers x and y
$=\sqrt{\text{xy}},$ if x and y both are irrational numbers
$=\sqrt{\text{xy}},$ if x is rational number and y is irrational number
$=\sqrt{\text{xy}},$ if x × y is not a perfect square and x, y both are rational numbers
3 irrational numbers are-
0.73073007300073000073... 0.75075007500075000075... 0.790790079000790000...
Concept Insight: There is infinite number of rational and irrational numbers between any two rational numbers. Convert the number into its decimal form to find irrationals between them.
Alternatively following result can be used to answer:
Irrational number between two numbers x and y
$=\sqrt{\text{xy}},$ if x and y both are irrational numbers
$=\sqrt{\text{xy}},$ if x is rational number and y is irrational number
$=\sqrt{\text{xy}},$ if x × y is not a perfect square and x, y both are rational numbers
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A company selected 2400 families at random and surveys them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below:
If a family is chosen, find the probability that the family is:
|
Monthly Income
(in ₹)
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Vechicles Per Family
|
|||
|
0
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1
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2
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Above 2
|
|
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Less than 7000
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10
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160
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25
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0
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7000 – 10000
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0
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305
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27
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2
|
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10000 – 13000
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1
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535
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29
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25
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|
13000 – 16000
|
2
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469
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29
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25
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|
16000 or more
|
1
|
579
|
82
|
88
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