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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

201 Views

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

$2 over 11$

2 over 11

11 right parenthesis space 2.0000 space left parenthesis space 0.1818 space..... space space space space bottom enclose space 11 space space end enclose space space space space space space space 90 space space space space space bottom enclose space space space 88 space space end enclose space space space space space space space space 20 space space space space space space bottom enclose space space 11 space space end enclose space space space space space space space space space 90 space space space space space space space bottom enclose space space 88 space space end enclose space space space space space space space space space space 2 therefore space space 2 over 11 space equals space 0.1818 space...... space equals space 0. top enclose 18.

The decimal expansion is non-terminating repeating.

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

329 over 400

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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

234 Views

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.

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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