Question

2.66666666.... - 0.999999999... in fraction​

Answer 1

(1)ANSWER OF 0.99999...SO ON

(2)ANSWER OF 2.666....SO ON

Answer:

a

b

=

4

15

the required fraction

Explanation:

Let

a

b

the unknown fraction

then

a

b

=

0.266666666

...

.

call this the 1st equation

Multiply both sides of the equation by 10 to produce

10

a

b

=

2.66666666

...

.

.

call this the 2nd equation

Go back to the 1st equation and this time multiply both sides by 100 to obtain

100

a

b

=

26.66666666

...

.

call this the 3rd equation

Now

subtract the 2nd from the 3rd

100

a

b

−

10

a

b

=

26.66666666

−

2.66666666

and we have

90

a

b

=

24

solve for a/b

a

b

=

24

90

=

4

15

a

b

=

4

15

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