Q1.Convert the following decimal into rational number of the form
p
:
q
.621
Q2. Find the decimal representation of
3
32
Q3. Convert the decimal 14.0052 to the rational number in its lowest form.
Q4. Give the decimal representation of the rational number 33/96 and tell whether it is
terminating or non-terminating.
Q5. State whether the following statements are true or false.
(i) The decimal representation of
1
is 0.5
3
(ii) If the denominator of a rational number which is in lowest terms has no prime
factors other than 2 or 5, the rational number has a terminating decimal
representation.
(iii)
If the denominator of a rational number which is in lowest terms has some
prime factors other than 2 or 5, the rational number has a non-terminating
repeating decimal representation.
Q6. Without actual division determine which of the following have a non-terminating
repeating decimal representation. Give reason. (Use the rule given in statements (ii) and
(iii) of Q.5)
(i) (i)
37
19
21
(ii)
(iii)
99
51
48
Q7. Find the difference between 0.28135 and
Q8 Express
9
32
15
in decimal fraction.
22
Q9. Find the value of 2.6 0.9
Q10. Express the following decimals in the form
p
( p and q being positive int egers q 0)
q
(i) 17.012 (ii) 1.251
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Q11. Convert 4.0013 int o a rational number of the form
p
q
Q12. Show that 0. 3 0. 37 0.70
Q13. Write .9999…. in the form p/q
Q14. Express
411
as a decimal.
160
Q15. Round off the following:
(i) 67. 4562 correct to 2 decimal places. (ii) 8.673459 x 100 correct to 3 decimal places.
Q16. Convert 335.140 to rational number in the lowest terms.
Q17. Can the following decimal numbers represent rational numbers? Give reason for
your answer.
(i) 0.010010001…….
(ii) 5.233344………
Q18. Which of the following statements is false?
(i)
1/25 is a terminating decimal.
(ii)
1/9 can be written as a terminating decimal.
(iii)
The decimal 0.8 is the same as the decimal 0.8000000
(iv)
The decimal representing 3/7 is a non-terminating repeating decimal.
Q19. Express
2
as a decimal fraction.
11
Q20. Convert the following rational numbers in their decimal form.
(i)
15
3186
(ii)
8
1250
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ANSWERS :
A1. 23/37
A2. 0.09375
A3.
35013
2500
A4. . 0.34375 (terminating)
A5. (i) False. (ii) True (iii) True.
A6. (i) and (ii) are Non- terminating repeating decimals.
Reason: If the denominator of a rational number which is in lowest terms has some
prime factors other than 2 or 5, the rational number has a non-terminating repeating
decimal representation.
(iii)Terminating decimal. Reason: If the denominator of a rational number which is in
lowest terms has prime factors no other than 2 or 5, the rational number has a
terminating decimal representation.
A7. 0.0001
A8. 0.6818
A9.
5
3
A10. (i)
A11.
4253
1251
(ii)
250
1000
39613
9900
A12. Convert both the numbers to the form p/q and then add.
A13. . 1
A14. 0.83
A15. (i) 67.46
A16.
(ii) 867.346
16757
50
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A17. (i) No. (ii) No. Reason: A non-terminating, non repeating decimal is not a rational
number.
A18. . (i) 1/25 = 0.04 terminating decimal. Hence True.
(ii) 1/9 = 0.1111…. non- terminating decimal. Hence False.
(iii) .8 = 0.8000000 True.
(iv) 3/7 = 0.428571428571…
0.428571. Hence True.
A19. 0.18
A20. (i) 1.875
(ii) 2.5488
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