Which rational number is equivalent to 3.90 with the .90 repeating?

A. 3/90
B. 39/10
C. 35/9
D. 43/11
EXPLAIN PLZ

let x = 3.909090...

multiply by 100 , (because I have 2 digits repeating, thus 2 zeros in 100, had there been 3 digits repeating, I would have mulitplied by 1000)

100x = 390.909090...

subtract the original:
99x = 390.9090... - 3.909090..
99x = 387
x = 387/99 = 43/11

thanks Reiny :))

To find the rational number that is equivalent to 3.90 with the repeating decimal .90, we can follow these steps:

Step 1: Let's denote the repeating decimal .90 as x.
x = 0.909090...

Step 2: Multiply x by 100 to remove the decimal point.
100x = 90.909090...

Step 3: Subtract x from 100x to eliminate the repeating part.
100x - x = 90.909090... - 0.909090...
99x = 90

Step 4: Now, divide both sides of the equation by 99 to solve for x.
99x/99 = 90/99
x = 90/99

Step 5: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
x = (10 * 9) / (11 * 9)
x = 10/11

Therefore, the rational number equivalent to 3.90 with the .90 repeating is 10/11.

Among the given options, the one that represents 10/11 is:
D. 43/11

Hence, the correct answer is D. 43/11.

To determine which rational number is equivalent to 3.90 with the .90 repeating, we need to convert the repeating decimal into a fraction.

Let x = 3.909090...
Then, multiplying both sides by 100, we get 100x = 390.909090...

Now, we subtract the original equation from the second equation to eliminate the repeating decimals:
100x - x = 390.909090... - 3.909090...
99x = 387

Divide both sides by 99 to solve for x:
99x/99 = 387/99
x = 387/99

Now, we need to simplify the fraction 387/99.
The greatest common divisor (GCD) of 387 and 99 is 3. Divide both the numerator and denominator by 3:
387/3 = 129
99/3 = 33

So, we have 129/33 as the simplified fraction.

Out of the given options:
A. 3/90 = 1/30
B. 39/10
C. 35/9
D. 43/11

B. 39/10 is equivalent to 3.90 with the .90 repeating.

Thus, the correct answer is B. 39/10.