Question

When 107/333 is written as a decimal, how many digits are in the smallest sequence of repeating digits?

a) 1
b)2
c) 3
d)4

Answer 1

107/333 = 0.32132132...

Answer: c

Answer 2

C) 3 Digits

Explanation:

In this question we are given a fraction
`\displaystyle(107)/(333)`.

We need to find the decimal expansion of this fraction and find the repeating digits.

Terminating and repeating fractions are the fractions whose value or decimal expansion does not end and the expansion have repeating digits.

If we evaluate the value of given fraction,

`\displaystyle(107)/(333) = 0.321321321...`

We can see that the decimal expansion does not end and the digits 321 are repeating itself.

This number can also be written as
`\bold{0.\overline{321}}`

Thus, there are three digits in the sequence of digits that repeat themselves.