Question

‌கீ‌ழ்‌க்காணு‌ம் தசம எ‌ண்களை p/q (‌p, q∈Z ம‌ற்று‌ம் q≠0) வடி‌‌வி‌ல் மா‌ற்றுக
i) 0.¯3
(ii) 2.¯124
(iii) 0.4¯5
(iv) 0.5¯68

Answer 1

Answer:

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Answer 2

விளக்கம்:

$\text { (i) } 0 . \overline{3}$

$x=0.3=0.3333....$    (1)

(1) * 10 = $10 x=3.333 \ldots$ (2)

(2) - (1)

10 x - x = 3.333 - 0.3333

9 x  = 3

$x=\frac{1}{3}$

ii) $2 . \overline{124}$

$x=2 . \overline{124}$

$=2.124124124....$(1)    

(1) *1000

$1000 x=2124.12412414 \ldots$  (2)

$(2)-(1) = 999 x=2122$

$x=\frac{2122}{999}$

iii) $0.4 \overline{5}$

$x=0.4 \overline{5}$

   = 0.4555555.......(1)

10 x = 4.55555....(2)

100 x = 45.5555...... (3)

(3) - (2) = 45.5555 - 4.5555

90 x = 41

$x=\frac{41}{90}$

iv) $0.5 \overline{68}$

x = $0.5 \overline{68}$ ........(1)

10 x = 5.686868....(2)

1000 x = 568.6868...(3)

(3) - (2) = 568.6868 - 5.6868

900 x = 563

 $x=\frac{563}{990}$