Question

Which of the following rational numbers lies between 1/10 and 1/4 ? *
a 1/5
b 1/20
c 2/5
d 1/10​

Answer 1

a.1/5

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Answer 2

Solution :-

writing the given numbers in decimal form we get,

→ 1/10 = 0.1 = 0.10

→ 1/4 = 0.25

now, checking all given options which number lies between 0.10 and 0.25 we get,

a) 1/5

→ 1/5 = 0.20

as we can see that,

→ 0.10 < 0.20 < 0.25

since 0.20 lies between 0.10 and 0.25 . Therefore, we can conclude that, (a) 1/5 lies between 1/10 and 1/4 .

b) 1/20

→ 1/20 = 0.05

since 0.05 does not lies between 0.10 and 0.25 . This number is not possible .

c) 2/5

→ 2/5 = 0.4 = 0.40

since 0.4 is greater than 0.25 . It does not lies between 0.10 and 0.25 . This number is not possible .

d) 1/10

→ 1/10 = 0.1 = 0.10

since 0.10 is equal to 0.10 . It does not lies between 0.10 and 0.25 . This number is not possible .

Hence, Option (a) is correct answer .

Method 2) :- By making denominator same .

→ 1/10 = (1/10) * (2/2) = (2/20)

→ 1/4 = (1/4) * (5/5) = (5/20)

checking given options now,

a) 1/5

→ (1/5) = (1/5) * (4/4) = (4/20)

as we can see that,

→ (2/20) < (4/20) < (5/20)

therefore, we can conclude that, (a) (1/5) lies between (1/10) and (1/4) .

b) 1/20

since,

→ 1/20 < 2/20

as we can see that, (1/20) is smaller than (2/20) therefore it does not lies between (1/10) and (1/4) .

c) 2/5

→ (2/5) = (2/5) * (4/4) = (8/20)

since,

→ (4/20) < (8/20)

as we can see that, (8/20) is greater than (4/20) therefore it does not lies between (1/10) and (1/4) .

d) 1/10

→ 1/10 = (1/10) * (2/2) = (2/20)

as we can see that, (2/20) is equal to (2/20) , therefore it does not lies between (1/10) and (1/4) .

Hence, Option (a) 1/5 is correct answer .

Learn more :-

let a and b positive integers such that 90 less than a+b less than 99 and 0.9 less than a/b less than 0.91. Find ab/46

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