Answer :
Answer:
[tex] \frac{29}{9} [/tex]
Step-by-step explanation:
3.2 repeating = 3.2222....
let's make it equal to x
x = 3.2222....
we want to eliminate the infinitely repeating digits, so let's multiply 3.2222.... by 10 and equate it to 10x
3.2222.... × 10 = 32.2222....
10x = 32.2222....
Now we have
x = 3.2222....
10x = 32.2222....
They both have an infinite number of repeating twos so subtract x from 10x to get rid of the repeating digits after the decimal point
Rewriting it as
10x = 32.2222....
x = 3.2222....
10x - x = 9x and 32.2222.... - 3.2222.... = 29
equate both
9x = 29
divide both sides by 9
x = 29/9