As we are aware of an astronomical year is, on average, 365 days, 5 hours, 48 minutes and 45 seconds. Translating this into minutes, we find that
365 days/year * 1440 minutes/day + 5 hours * 60 minutes/hour
+ 48 minutes + 45 seconds / 60 seconds/minute = 525948.75 minutes/year
To calculate how many of these there are in a year: multiply by the number of years you want to know about. If you wanted to know how many such ‘astronomical’ minutes there were in a century (100 years), you’d have:
525948.75 x 100 = 525994750 astronomical minutes per century. To convert this into ‘clock’ minutes, multiply by 1440 (the number of minutes in a 24-hour day): 525994750 x 1440 = 7195180000 clock minutes per century.
Knowing that there are 60 seconds in a minute, 12 hours in an hour and 24 hours in a day, you can convert this to seconds – the result is 914341640800 seconds per century. Dividing by 60 differentiates between clock seconds (sixtieths of second) and astronomical seconds (sixtieths of an astronomical day), which turns out to be 1.324868762112E+15 clock sixtieths per century, or 13244866937500 clock sixtieths per century. Dividing by 60 once more we end up with 1.982647188677E+18 clock seconds per century, or 189803044000000 clock seconds per century: 90 NEW YEARS PER SECOND!
So there you have it: one astronomical year is 525994750 minutes; this is converted to 914341640800 seconds; and this is turned into 189803044000000 clock seconds – which means that a new year (ignoring leap years) only comes around every 90 of those!