Final answer:
To add a decimal to a fraction containing a decimal and a variable, convert the fraction to a decimal and then add the decimals, respecting the rules of significant figures and decimal places. In scientific notation, adjustments include moving the decimal and modifying the exponent. If x is unknown, the expression remains as an expression.
Step-by-step explanation:
To add a decimal to a fraction that contains a decimal and a variable, like -9.1 + x/3.1, you first want to convert all numbers to a common form. For ease, convert the fraction to a decimal by dividing x by 3.1. If possible, it's helpful to convert these to fractions with the same denominator or work with the decimals directly if you are comfortable with decimal arithmetic.
Next, you can simply add the decimals together. Keep in mind the rules of significant figures and decimal places. When adding or subtracting, the result should not have more decimal places than the number in the problem with the least number of decimal places.
If we imagine x is replaced by a specific number, you would perform the following operations: divide x by 3.1 to convert the fraction to a decimal, then combine it with -9.1 by adding the two decimal values together.
If you cannot replace x with a specific number because it is a variable representing an unknown value, then the expression remains as an expression and cannot be simplified further unless more information about x is given.
Remember, when dealing with scientific notation, adding exponents occurs only when multiplying numbers with like bases, and subtracting exponents when dividing with like bases. Also, changing the form of a number to scientific notation requires moving the decimal point and adjusting the exponent accordingly.