Quadrillion

From Academic Kids

The quadrillion is a large number which has one of two values depending on how or where it is being used. Quadrillion comes after trillion.

Contents

Short scale usage

In short scale usage, a quadrillion is equal to a 1 with 15 zeroes, namely: 1,000,000,000,000,000 (1015)

It is a thousand trillion (short scale), i.e. a thousand million million. The SI prefix for this number is peta.

Long scale usage

In long scale usage, a quadrillion is equal to a 1 with 24 zeroes, namely: 1,000,000,000,000,000,000,000,000 (1024)

It is a million trillion (long scale), i.e. a million million million million. The SI prefix for this number is yotta.

While people in the British Isles, Australia and New Zealand traditionally employed the long scale usage, they have largely switched to the short scale usage.

Properties

Quadrillion is the lowest natural number with a "q" in it's name. A quadrillion has 255 proper divisors, and also a 255-gon is constructible since it is the product of the Fermat primes 3, 5, and 17. The divisor function calculated on a quadrillion is equal to:

<math> \sigma(10^{15})\;=\;2,499,961,853,010,960<math>

and therefore its abundancy is 499,961,853,010,960, which is almost half of a quadrillion. The divisor function of a quadrillion (and indeed, of all high powers of ten) may be calculated with the formula:

<math> \sigma(10^n)\;=\;\frac{(2^{n+1} - 1)(5^{n+1} - 1)}{4}<math>

which may be seen by applying the formula for the partial sum of a geometric series twice to the sum of the divisors.

See also

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