Question

Investigate what happens with the “ninth” fractions.

E.g. what do you get for 1/9, 2/9, 3/9 etc.

Have you spotted a pattern?

What would 9/9 be as a decimal?

Answer 1

Given:

Fractions
`(1)/(9),(2)/(9),(3)/(9)` etc.

To find:

What happens with the “ninth” fractions.

Solution:

We have, the values of
`(1)/(9),(2)/(9),(3)/(9)` are

`(1)/(9)=0.11111...`

`(2)/(9)=0.22222...`

`(3)/(9)=0.33333...`

Clearly we can spot a pattern, because after decimal the numerator digit of fraction is repeating.

Similarly,

`(9)/(9)=0.99999...`

Therefore, the decimal value of
`(9)/(9)` is 0.99999..., which is approximately 1.