Question

The decimal 0.3(repeating) represents 1/3. what type of number best describes 0.9(repeating), which is 3 times 0.9(repeating)? explain.

Answer 1

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Answer 2

Explanation:

Given that the decimal 0.3 (repeating) represents
`(1)/(3)`

We are to find out the value 0.9(repeating) using the above.

Since
`0.9999... = 3 (0.3333...)\\0.9999... = 3((1)/(3) ) =1`

We can solve this using the other method also

Let

`x = 0.9999....\\\\ 10x = 9.9999....\\--------------------\\9x = 9\\x=1`

We get the same answer under both the methods.