An engineer should have something mathematical on his website, so here is some math trivia for you.

Repeating Decimals

Here is a curious math conundrum for you. What happens when you divide any whole number by 16.5?

Get out your calculator and try a few.

OK, now let me try some and see what happens:

20 / 16.5 = 1.21212121 . . .

39 / 16.5 = 2.36363636 . . .

51 / 16.5 = 3.09090909 . . .

94 / 16.5 = 5.69696969 . . .

Aha! Repeating decimals. Looks like any number divided by 16.5 yields a repeating decimal.

But why should that be? Take a minute to try to figure it out.

Tick, tock, tick, tock, tick tock, tick, tock . . .

OK. Lets divide 33 by 16.5. It equals 2. This is also 2.0000000 . . . , which is also a repeating decimal. But it is also a whole number.

So the secret is that dividing any number by 16.5 is the same as dividing by half of 33. Since 33 is 11 times 3, it's just a multiple of 3, and any whole number divided by 3 gives you a repeating decimal. So numbers divided by multiples of 3 also give you repeating decimals. Isn't that curious?

Mathematicians find these number patterns interesting. If you don't, you're probably not cut out to be a mathematician. But, of course, there's nothing wrong with that.

PRIME

We recently experienced a whole year called 2011. Did you know that 2011 is a PRIME NUMBER?

What's a prime number? Any integer that is only divisible (without a remainder) by the number one and itself.

If you start counting at zero, the prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, . . . .

Note that 2 is the only even prime number.

If the prime number is greater than 5, the only digits allowed in the ones column are 1, 3, 7, and 9.

Despite this limitation, there are an infinite number of prime numbers, which means that no matter how big a prime number you find, there will always be a larger one.

Was the year of your birth a prime number? Yes, if you were born in any of the following years:

1879, 1889, 1901, 1907, 1913, 1931,

1933, 1949, 1951, 1973, 1979, 1987,

1993, 1997, 1999, 2003, 2011, 2017.

This is a span of 138 years, which contains a mere 15 prime numbers, a little more than a tenth of the total.

The smallest interval between adjacent prime numbers in this particular list is 2, the largest is 22.

If you were born in 1879, you are 132 years old, which means that you died a few years ago. If you were born in 2017, you haven't been born yet, which means you are trying to fool me.

If you have some interesting fact about prime numbers, send me an email and I may decide to mention it here.

Later, John.

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Last Updated ( Tuesday, 17 January 2012 16:55 )