1. What is an irrational number?
2. How is interest that is continuously compounded different from interest that is compounded every half year? every quarter year?
2006-10-19 01:01:03 · 3 answers · asked by mochaspice16 1 in Science & Mathematics ➔ Mathematics
An irrational number is one that cannot be expressed by a ratio. That means you can't show it as a fraction, or as a decimal. You can apprxomiate it those ways, but never exactly.
Interest compounded continuously will grow faster, because the interest starts earning interest instantly. Every year means the interest is added at the end of 365 days, and then starts earning.
Integral Calculus (and the value of e) let you figure those values exactly so you can compare them. There isn't a big difference between continuously and monthly, but it's appreciable between continuously and yearly.
2006-10-19 01:10:31 · answer #1 · answered by Iridium190 5 · 0⤊ 0⤋
Modifying what another person already wrote: an irrational number is any number that can't be expressed as the ratio (fraction) of *two integers.*
If you leave out that part of the definition, it becomes useless, because any number, even something like Ï or â2, can be made into a fraction by just writing it over a denominator of 1.
2006-10-19 09:33:13 · answer #2 · answered by Jay H 5 · 0⤊ 0⤋
wikipedia FTW!
2006-10-19 08:08:05 · answer #3 · answered by caladbolg 1 · 0⤊ 0⤋