2.2: Really Big and Really Small Numbers
- Page ID
- 50936
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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).
|
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.
|
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
- References (4)
Contributors and Attributions
Saburo Matsumoto
CC-BY-4.0