Final answer:
The expression 11.9 + 0.888... + 0.1888... can be expressed in the form of p/q as 1071/990. To do this, repeating decimals are converted to fractions and then added together with a common denominator.
Step-by-step explanation:
Yes, we certainly can express 11.9+0.888...+0.1888... in the form of p/q. First, let's express 0.888... and 0.1888... as fractions. These are examples of repeating decimals, which can be represented as a fraction. For 0.888..., let's let x=0.888.... Therefore, 10x=8.888..., so if we subtract the original equation from this (10x - x = 8.888... - 0.888...), we get 9x = 8, which simplifies to x = 8/9. So, 0.888... equals 8/9. Using a similar process, 0.1888... equates to 2/11.
Now, we simply add these fractions to the given number. So, the expression 11.9 + 0.888... + 0.1888... becomes 11.9 + 8/9 + 2/11. 11.9 as a fraction is 119/10, so the expression is now 119/10 + 8/9 + 2/11. To add these, we need a common denominator. A common denominator for 10, 9, and 11 is 990. Therefore, our expression becomes 1071/990 when simplified, so in the form p/q, your answer is 1071/990.
Learn more about Repeating Decimals to Fractions