Question

Find the value of:
0.9999..+ 0.666666.​

Answer 1

$\huge \bf\binom{ \: \: \: \: \: 0.9999999}{ \: \: + 0.6666666} \\ \huge \bf \: = 1.6666665$

Answer 2

Answer:

5/3

Step-by-step explanation:

0.9999... + 0.6666...

Just add first 3 digits(999 + 666) after decimal, it would be 1665. As we know given number doesn't terminate, 5 would never come and it will be

0.999... + 0.666.. = 1.666...

Let 1.666... = x, we say this '1.6 bar = x'.

=> 1.6 = x ...(1)

Multiply both sides by 10:

=> 16.6 = 10x ...(2)

Subtract (1) from (2):

16.6 = 10x

- 1.6 = - x

15.0 = 9x [bar cancelled]

=> 15 = 9x

=> 5/3 = x

Thus, 0.999... + 0.666.. = 5/3

Moreover, you can solve 0.999... and 0.666... individually and then add.

Solve using the same technique 'let no. = x, multiply both sides by 10ⁿ where n is the digits before bar no., here it is 0, and follow as done above).

0.999... = 1 & 0.666... = 2/3

Thus, 0.999... + 0.666... = 5/3