Question

1.121212... is equivalent to what as a mixed number? option a112/99option b37/33option c1 4/33option d1 13/33hi not sure if the pic helps but im just confused and was hoping for some help?

Answer 1

1 4/33

Since 1.121212... is a composite repeating number then we can convert this into a fraction

1) 1.121212....

Underlining the repeating part :

1.121212....

So we can count two different digits 1 and 2, so we can write it as a fraction, placing on the denominator 99 for we have two different numbers, and then subtract 112 -1 on the numerator:

`1.121212\text{ =}(111)/(99)=(37)/(33)`

2) Transforming into a mixed number

Since the question asks us to convert it to Mixed number, then we have to keep the denominator, 33,

For the numerator, we pick the 37 and divide it by 33 and place the quotient

37 : 33 = Quotient 1 Remainder : 4

Place the Quotient 1 beside a fraction with the remainder as the new numerator like this:

`(37)/(33)\text{ = 1}(4)/(33)`