Determine the value of $0 . 68 ¯ + 0. 73 ¯$ .

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14199

14399

147990

None of these

answer is A.

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Detailed Solution

We are given two recurring decimal numbers as

0 . 68 ¯ + 0. 73 ¯

and we need to determine the sum.
To do so, we need to first convert both the recurring decimals as a rational number in its simplest form and then add them.
Now, let us assume

0. 68 ¯

to be x.
It can be written in the expanded form as follows,

x = 0 ⋅ 686868.......

……….. (i)
So, it can be observed that the repeating part of the decimal has two digits.
So, shift it by two places towards the left of the decimal, by multiplying each side of equation (1) by 100 as follows,

100 x = 68 ⋅ 686868.....

…………. (ii)
Now, to get the required rational number, we will subtract equation (ii) from (i) and simplify as follows,

100 x − x = 68.686868..... − 0.686868..... 99 x = 68 x = 6899

So, from equation (i), we have

0. 68 ¯ = 6899

.
Next, let us assume

0. 73 ¯

to be x.
Now, it can be written in the expanded form as follows,

x = 0 ⋅ 737373.......

……….. (iii)
So, it can be observed that the repeating part of the decimal has two digits.
So, shift it by two places towards the left of the decimal, by multiplying each side of equation (1) by 100 as follows,