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
Answers
Answer:
a
Step-by-step explanation:
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Solution :-
writing the given rational numbers in decimal form we get,
→ 1/10 = 0.1 = 0.10
→ 1/4 = 0.25
now, checking all given options which rational 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) 1/5 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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