Final answer:
The reduced fraction that corresponds to the decimal expansion 0.05050 is 1/20. This is found by converting the decimal into the sum of two fractions, 53/1000 and 1/2000, and then simplifying that sum to 1/20.
Step-by-step explanation:
To identify the reduced fraction that has the decimal expansion 0.05050, we first recognize that the repeating decimal portion is 05, thus suggesting that the fraction will have a denominator which is a multiple of 99 to represent the recurring nature. However, the decimal given does not strictly follow this pattern, as there is a single zero following the decimal point before the repeating pattern begins.
To convert this particular decimal to a fraction, we realize that the number is the same as 0.05 repeated, or ⅓/1000 (53 thousandths). Since the repeating decimal is 05, or 5 hundredths, and considering that the non-repeating part is 0.00050 (which is equivalent to 1/2000), we can find a common denominator for these two values to combine them into a single fraction.
Combining ⅓/1000 and 1/2000 provides us with 1/20 as the simplified fraction, since 53 + 1 equals 54, and 54/2000 simplifies to 27/1000, which then simplifies further to 1/20 when divided by 27. Therefore, the option (1) 1/20 is the correct reduced fraction for the decimal expansion 0.05050.