2.2: Really Big and Really Small Numbers

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Globally, there is no absolute agreement on what to call large numbers. ‘One million’ is expressed as 1,000,000, but Americans express ‘one billion’ as 1,000,000,000. This is the same as \(10^9\), or one followed by nine zeros. In the UK, however, \(10^9\) may be called ‘one thousand million.’ So, in the UK, it may be \(10^{12}\) that represents ‘one billion’ but for Americans, that would mean ‘one trillion.’ (It should be noted some British people are beginning to adopt the American naming system.)

Now, in India, they may use commas after two zeros as opposed to three when counting higher than 1,000. So, the Indian system calls 100,000 (one hundred thousand) one lakh and 10,000,000 (ten million) is called one crore.

In many Asian countries, large numbers have names based on 10,000s rather than 1,000s. Yes, large and small numbers can be quite confusing.

The following table describes the standardized and scientific names in the American system for very large and very small numbers. Understanding your properties of exponents and exponent tables will help you interpret this. (Note: This table uses metric prefixes. EX: 1000 meters = 1 kilometer).

Table \(\PageIndex{1}\): Big Numbers
Number	Name	Metric Prefix
\(10^1=10\)	Ten	deka-
\(10^2=100\)	Hundred	hecto-
\(10^3=1000\)	Thousand	kilo-
\(10^4=10,000\)	Ten Thousand	myria-
\(10^6=1,000,000\)	One Million	Mega-
\(10^9=1,000,000,000\)	One Billion	Giga-
\(10^{12}\)	One Trillion	Tera-
\(10^{15}\)	One Quadrillion	Peta-
\(10^{18}\)	One Quintillion	Exa-

By the way, \(10^{100}\), a one followed by 100 zeros is actually named “googol.” Note that this spelling is different from the name of a large tech company.

Table \(\PageIndex{2}\): Small Numbers
Number	Name	Metric Prefix
\(10^{-1}=0.1\)	One Tenth	deci-
\(10^{-2}=0.01\)	One Hundredth	centi-
\(10^{-3}=0.001\)	One Thousandth	milli-
\(10^{-6}=0.000001\)	One Millionth	micro-
\(10^{-9}=0.000000001\)	One Billionth	nano-
\(10^{-12}\)	One Trillionth	pico-
\(10^{-15}\)	One Quadrillionth	femto-
\(10^{-18}\)	One Quintillionth	atto-

Reference

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Contributors and Attributions

Saburo Matsumoto
CC-BY-4.0