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
To find the rational number equivalent to 3.90 with the .90 repeating, we need to convert the repeating decimal into a fraction.
Let's represent the repeating decimal as x:
x = 0.909090...
To get rid of the repeating decimal, we can multiply both sides of the equation by a power of 10. Since there are two digits after the decimal point that are repeating (90), we multiply both sides by 100:
100x = 90.909090...
Now, we want to eliminate the decimal part of the repeating decimal, so we subtract x from both sides of the equation:
100x - x = 90.909090... - 0.909090...
99x = 90
x = 90/99
Therefore, the rational number equivalent to 3.90 with the .90 repeating is 90/99.
Now, let's examine the answer choices:
A. 3/90 represents a fraction with both the numerator and denominator divisible by 3, so it can be simplified to 1/30. This is not equivalent to 3.90 with .90 repeating.
B. 39/10 can be simplified to 3.9, however, it does not have the repeating part.
C. 35/9 is not equivalent to the given decimal.
D. 43/11 is also not equivalent to the given decimal.
Therefore, the correct answer is none of the options provided. The equivalent rational number to 3.90 with the .90 repeating is 90/99.
Divide the numerators by the denominators to find your answer.
Example: 3/90 = 0.033333 >> Nope that's not it.