MATH 328 Productive Failure 1

The mistake I made on this problem from Quiz 2 had to do with mindlessly forgetting what expanded form meant in the moment. Since we had not talked about expanded form yet this quarter I quickly blanked even though this was a concept we went over time and time again in MATH 227 with numbers in different bases. Although I initally accounted for the fractional representation of 0.3806 and was able to understand that it could be written as 3806 x 10^-4, I did not even think about writing it in the correct expanded form by accounting for each place value as a base 10 to the negative power of whatever place value it is in. This correction aided me in the lesson following the quiz where we were instructed to convert decimals into different bases. Through this correction and representation in expanded form I was able to better understand exactly what each number in the decimal was representing. For example the three in the tenths place representing three 1/10's (or 10^-1). From this mistake I was able to recall what we learned last quarter and apply it to the concepts we are working with now and also able to make sense of what each number in different place values represents in a fractional sense.