Unemployment remained relatively stable in Nevada County in December, fluctuating one-tenth of a percentage point since October, part of a California economy that remains near the top of the country’s list of states with high percentages of people seeking jobs. While Nevada County’s seasonably unadjusted unemployment rate dropped one-tenth of a percentage point from November’s 8.8 percent to December’s 8.7 percent, a number that matches October’s percentages, California’s jobless rate increased to 9.7 percent in December, up from 9.6 percent in November, according to the state’s Employment Development Department said Friday. While the state’s unemployment has remained relatively steady since …