Standard Form

Background

The search for amazing facts about very large and very small numbers is fascinating. Some examples from the programme were:

• Rate of delivery of junk mail in the US = 4.4 x 10² kg/s
• Number of bacteria in a site of gum disease = 1 x 10¹⁰
• Mass of the smallest known virus = 9.5 x 10^-21 kg

Pupils can find their own favourite facts. A large list of physics-related facts given in standard form can be found at:
http://prisma.foe.calpoly.edu/physmag.html

Millions and millions

People are often confused when they hear words like 'millions' and 'billions'. There is more than one system in use. Traditionally one system is used in the UK (and Germany) and another in the USA (and France).

In the British system a billion is a million million and a trillion is a million million million. In the American system a billion is a thousand million and a trillion is a thousand billion (so an American trillion is equal to a British billion).

There is a tendency now to adopt the American terminology worldwide.

	British	American
103	thousand	thousand
106	million	million
109	thousand million	billion
1012	billion (= million2)	trillion
1015	thousand billion	quadrillion
1018	trillion (= million3)	quintillion
1021	thousand trillion	sextillion
1024	quadrillion (= million4)	septillion
1063	thousand decillion	vigintillion
10100	googol	googol
10googol	googolplex	googolplex

Did you know...?

The number of grains of sand on all the beaches of the world has been estimated at 10²⁴.

Sir Arthur Eddington estimated the number of particles in the Universe at 10⁷⁹.

The number of humans who have ever lived on Earth is estimated at 10¹⁰.

The human brain contains about 10¹⁰ cells (neurons).

What is the largest number that can be written using only three digits? The most common answer is 999. But what about 9⁹⁹, or (9⁹) raised to the power of 9, or 9 raised to the power of 9⁹...? The last number is equal to 9^387420489, which has 369,693,100 digits.