Historically, different people have defined a year in different ways. For example, an Egyptian year is 365 days long, a Julian year is 365\(\frac14\) days long, and a Gregorian year is 365.2425 days long.
To find the number of seconds in a year, multiply the length of the year in days by the number of seconds in a day.
To find how much shorter a Gregorian year is than a Julian year (as a percentage of a Julian year), divide the difference by the length of a Julian year: $$648 \div 31557600 = 0.00002053...$$ which is approximately \(\frac{2}{100,000}\) or 0.002%.
So a Gregorian year is about 0.002% shorter than a Julian year.
To find how much shorter a Gregorian year is than a Julian year (as a percentage of a Julian year), divide the difference by the length of a Julian year: $$648 \div 31557600 = 0.00002053...$$ which is 0.002053... %.
Rounding, we see that a Gregorian year is about 0.002% shorter than a Julian year.
Commentary
Many students will not know that when comparing two quantities, the percent decrease between the larger and smaller value is not equal to the percent increase between the smaller and larger value. Students would benefit from exploring this phenomenon with a problem that uses smaller values before working on this one.