Question

$solve \: the \: problem \: ple \alpha se$
​

Answer 1

Answer:

I) 0.3....

Let this number be x

x = 0.333.... eq (1)

mutilplying both sides by 10.

10x = 3.333..... eq(2)

Subtracting eq(2) by eq(1)

we get,

10x - x = 3.333....... - 0.333...

9x = 3

x = 3/9 = 1/3

Therefore 0.333…... = 1/3

(ii) 0.53....

Let this number be x

x = 0.5353.... eq (1)

mutilplying both sides by 100.

100x = 53.53..... eq(2)

Subtracting eq(2) by eq(1)

we get,

100x - x = 53.53...... - 0.53...

99x = 53

x = 53/99=

Therefore 0.5353..... = 53/99

(iii) 3.555...

Let this number be x

x = 3.555... eq (1)

mutilplying both sides by 10

10x = 35.555.... eq(2)

Subtracting eq(2) by eq(1)

we get,

10x - x = 35.555...... - 3.555..

9x = 32

x = 32/9

Therefore 3.555..... = 32/9

(iv) 4.66......

Let this number be x

x = 4.66.... eq (1)

mutilplying both sides by 10.

10x = 46.66..... eq(2)

Subtracting eq(2) by eq(1)

we get,

10x - x = 46.66....... - 4.66..

9x = 42

x = 42/9 = 14/3

Therefore 4.66.... = 14/3

(v) 0.99999.......

Let the number be x

x = 0.99999..…..eq(1)

mutilplying both sides by 10.

10x = 9.9999.... eq(2)

Subtracting eq(2) by eq(1)

we get,

10x - x = 9.9999....... - 0.99999..

9x = 9

x = 1

Therefore 1 = 0.99999

(vi). 2.23444.....

Let the number be x

x = 2.23444..…..eq(1)

mutilplying both sides by 100

10x = 22.3444.... eq(2)

Subtracting eq(2) by eq(1)

we get,

10x - x = 22.34444....... - 2.23444..

9x = 20.11

x = 2011/90

Therefore 2011/90 = 2.23444.....

Hope it helps ☺️