Show that 0.3333..... = can be expressed in the form where p

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Number Systems

Short Answer Type

51. Find one irrational number between the numbers a and b given below:

a = 0.1111 ........ =

0. top enclose 1

b = 0.1101.

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52. Find two rational numbers in the form

straight p over straight q

between 0.34 344 3444 34444 3 ...... and 0.36 366 3666 36666 3......

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53. Express

5. top enclose 347

in the form

straight p over straight q

where p and q are integers and q ≠ 0.

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54.

Express $0. top enclose 001$ in the form of $straight p over straight q$ where p and q are integers and q ≠ 0.

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55. Express

5. top enclose 2

in the form of

straight p over straight q comma

where p and q are integers and q ≠ 0.

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56. How many irrational numbers lie between

square root of 2

and

square root of 3 ?

Find any three irrational numbers lying between

square root of 2

and

square root of 3.

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57. Find two irrational numbers between

1 over 7

and

2 over 7.

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58. Find the decimal expansions of

10 over 3 comma space 7 over 8 space a n d space 1 over 7

and

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59. Show that 3.142678 is a rational number. In other words, express 3.142678 in the form

straight p over straight q

where p and q are integers and q ≠ 0.

open square brackets Hint space colon space 3.142678 equals 3142678 over 1000000 close square brackets

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60. Show that 0.3333..... = $0. top enclose 3$ can be expressed in the form $straight p over straight q$ where p and q are integers and q ≠ 0.

Solution not provided.

Ans. $1 third$

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