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Number Systems

Short Answer Type

31. Write the following in decimal form and say what kind of decimal expansion each has:

3 over 13

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32. Write the following in decimal form and say what kind of decimal expansion each has:

2 over 11

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33. Write the following in decimal form and say what kind of decimal expansion each has:

329 over 400

158 Views

34. You know that

1 over 7 equals 0. top enclose 142857

Can you predict what the decimal expansions of

2 over 7 comma space 3 over 7 comma space 4 over 7 comma space 5 over 7 comma space 6 over 7

are, without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of

1 over 7

carefully.]

281 Views

35. Express the following in the form

straight p over straight q

where p and q are integers and q ≠ 0.

left parenthesis straight i right parenthesis space 0. top enclose 6

364 Views

36. Express the following in the form

p over q

where p and q are integers and q ≠ 0.

0. top enclose 47

320 Views

37. Express the following in the form

straight p over straight q

where p and q are integers and q ≠ 0.

0. top enclose 001

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38. Express 0.99999...... in the form $straight p over straight q comma$ Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Let x = 0.99999......
Multiplying both sides by 10 (since one digit is repeating), we get

10x = 9.9999 .........
$rightwards double arrow$ 10x = 9 + 0.99999 ......
$rightwards double arrow$ 10x = 9 + x
$rightwards double arrow$ 10x - x = 9
$rightwards double arrow$ 9x = 9

$rightwards double arrow space$ $x equals 9 over 9 equals 1$
Thus, 0.99999 ....... = 1 = $1 over 1$

Here, p = 1
q = 1

Since 0.99999......goes on for ever, so there is no gap between 1 and 0.99999......and hence they are equal.

266 Views

39. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of

1 over 17 ?

Perform the division to check your answer.

232 Views

40. Look at several examples of rational numbers in the form

straight p over straight q left parenthesis q not equal to 0 right parenthesis comma

where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

430 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

38. Express 0.99999...... in the form Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

38. Express 0.99999...... in the form $straight p over straight q comma$ Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.