Powers of Ten

本文介绍了非常大的数和非常小的数的表示方法,以及它们在实际应用中的例子,如距离单位、质量单位和能量单位等。

VERY LARGE NUMBERS:

"in words"

  

"in words"

One1001."ten to the zero"
ten10110."ten to the one"
hundred102100."ten to the two"
thousand1031,000."ten to the three"
ten thousand10410,000."ten to the four"
hundred thousand105100,000."ten to the five"
million1061,000,000."ten to the six"
ten million10710,000,000."ten to the seven"
hundred million108100,000,000."ten to the eight"
billion1091,000,000,000."ten to the nine"
ten billion101010,000,000,000."ten to the ten"
hundred billion1011100,000,000,000."ten to the eleven"
trillion10121,000,000,000,000."ten to the twelve"
ten trillion101310,000,000,000,000."ten to the thirteen"
hundred trillion1014100,000,000,000,000."ten to the fourteen"
Names are on threes... on 3, 6, 9 (thousand, million, billion).   ,000,

The names "billion" and "trillion" mean different things in different countries. This is the US version.
There are a few more names after "trillion", but they are almost never used.

VERY SMALL NUMBERS:

"in words"

  

"in words"

One1001."ten to the zero"
tenth10-10.1"ten to the minus one"
hundredth10-20.01."ten to the minus two"
thousandth10-30.001."ten to the minus three"
ten thousand10-40.0001."ten to the minus four"
hundred thousandth10-50.00001."ten to the minus five"
millionth10-60.000001"ten to the minus six"
ten millionth10-70.0000001."ten to the minus seven"
hundred millionth10-80.00000001."ten to the minus eight"
billionth10-90.000000001."ten to the minus nine"
ten billionth10-100.0000000001."ten to the minus ten"
hundred billionth10-110.00000000001."ten to the minus eleven"
trillionth10-120.000000000001"ten to the minus twelve"
ten trillionth10-130.0000000000001."ten to the minus thirteen"
hundred trillionth10-140.00000000000001."ten to the minus fourteen"

EXAMPLES of LARGE NUMBERS:

1 AU = 150,000,000 km = 1.5x l08 km = 9.2 x l07miles
Mass of the Sun = 1 Solar Mass = 2.0 x 1030 kg
1 kilometer      = 1 km = 103 m  ~ 5/8 mile

Energies of Fermilab's Chain of Accelerators:
Cockroft Walton:  750 KeV (Kilo-electron volts, thousand electron volts)
    = 750 times 103 electron volts 
Linac (Linear Accelerator): 400 MeV ( Mega electron volts, million electron volts)
    = 400 times 106 electron volts
Booster, Recycler, Debuncher, Accumulator accelerators:
          8 GeV (Giga-electron volts, billion (U.S.) electron volts)
        = 8 times 109 electron volts
Main Injector:  150 GeV = 150 x = 1.5 x 1011 electron volts
Tevatron: 0.98 TeV (Tera electron volts, trillion electron volts) = nearly 1012 electron volts
109 electron volts

EXAMPLES of SMALL NUMBERS:

1 centimeter     = 1 cm = 10-2 m  ~ 2/5 inch width of a pen
1 millimeter     = 1 mm = 10-3 m  ~ 1/25 inch width of lead in pencil
1 micrometer  =  1 micron  =  10-6
           High power microscopes look at objects as small as a few micrometers
1 microsecond = 10-6 seconds
          The lifetime of a mu-lepton is about 2 microseconds
1 nanosecond = 10-9 seconds
          A pi-meson lives on the average for 26 nanoseconds
         
A particle at the speed of light travels about one foot in one nanosecond. 

  http://www-bd.fnal.gov/public/powers.html
【评估多目标跟踪方法】9个高度敏捷目标在编队中的轨迹和测量研究(Matlab代码实现)内容概要:本文围绕“评估多目标跟踪方法”,重点研究9个高度敏捷目标在编队飞行中的轨迹生成与测量过程,并提供完整的Matlab代码实现。文中详细模拟了目标的动态行为、运动约束及编队结构,通过仿真获取目标的状态信息与观测数据,用于验证和比较不同多目标跟踪算法的性能。研究内容涵盖轨迹建模、噪声处理、传感器测量模拟以及数据可视化等关键技术环节,旨在为雷达、无人机编队、自动驾驶等领域的多目标跟踪系统提供可复现的测试基准。; 适合人群:具备一定Matlab编程基础,从事控制工程、自动化、航空航天、智能交通或人工智能等相关领域的研究生、科研人员及工程技术人员。; 使用场景及目标:①用于多目标跟踪算法(如卡尔曼滤波、粒子滤波、GM-CPHD等)的性能评估与对比实验;②作为无人机编队、空中交通监控等应用场景下的轨迹仿真与传感器数据分析的教学与研究平台;③支持对高度机动目标在复杂编队下的可观测性与跟踪精度进行深入分析。; 阅读建议:建议读者结合提供的Matlab代码进行实践操作,重点关注轨迹生成逻辑与测量模型构建部分,可通过修改目标数量、运动参数或噪声水平来拓展实验场景,进一步提升对多目标跟踪系统设计与评估的理解。
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