8.9 带有计算器的科学说明

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 带有计算器的科学标记

  Collapse Expand

  带有计算器的科学标记

  播放段落

  Scientific Notation Using a Calculator 
  ::使用计算器的科学说明

  播放段落

  Let's look at some real-world applications involving scientific notation.
  ::让我们来看看一些现实世界的应用 涉及到科学符号。

  播放段落

  1. The mass of a single lithium atom is approximately one percent of one millionth of one billionth of one billionth of one kilogram. Express this mass in scientific notation.
  ::1. 单锂原子的重量约为每公斤10亿分之一的百万分之一的百分之一。

  播放段落

  We know that a percent is $\begin{array}{r}\frac{1}{100}\end{array}$ , and so our calculation for the mass (in kg) is:
  ::我们知道百分之1100是百分之1100, 所以我们对质量(千克)的计算是:

  $$\begin{array}{r}\frac{1}{100}\times \frac{1}{1,000,000}\times \frac{1}{1,000,000,000}\times \frac{1}{1,000,000,000}={10}^{-2}\times {10}^{-6}\times {10}^{-9}\times {10}^{-9}\end{array}$$

  播放段落

  Next we use the product of powers rule we learned earlier:
  ::接下来我们用我们早先学到的 权力的产物:

  播放段落

  $$\begin{array}{r}{10}^{-2}\times {10}^{-6}\times {10}^{-9}\times {10}^{-9}={10}^{((-2)+(-6)+(-9)+(-9))}={10}^{-26}kg.\end{array}$$

  
  ::10-2x10-6x10-9x10-9=10(-2)+(-6)+(-9)+(-9)+(-9)=10-26公斤。

  播放段落

  The mass of one lithium atom is approximately $\begin{array}{r}1\times {10}^{-26}kg\end{array}$ .
  ::一个锂原子的质量约为1x10-26千克。

  播放段落

  2. You could fit about 3 million $\begin{array}{r}E\end{array}$ . coli bacteria on the head of a pin. If the size of the pin head in question is $\begin{array}{r}1.2\times {10}^{-5}{m}^2\end{array}$ , calculate the area taken up by one $\begin{array}{r}E\end{array}$ . coli bacterium. Express your answer in scientific notation
  ::2. 在针头上可以装上大约300万E.大肠杆菌。如果有关针头的大小为1.2x10-5平方米,计算一个E.大肠杆菌吸收的区域。用科学符号表示回答。

  播放段落

  Since we need our answer in scientific notation, it makes sense to convert 3 million to that format first:
  ::既然我们需要科学符号的答案,首先将300万改为这种形式是有道理的:

  $$\begin{array}{r}3,000,000=3\times {10}^6\end{array}$$

  播放段落

  Next we need an expression involving our unknown, the area taken up by one bacterium. Call this $\begin{array}{r}A\end{array}$ .
  ::接下来,我们需要一种表达方式, 涉及我们未知的, 一个细菌占据的区域。

  播放段落

  $$\begin{array}{rlrl}& 3\times {10}^6\cdot A=1.2\times {10}^{-5}& & -since3millionofthemmakeuptheareaofthepin-head\end{array}$$

  
  ::3x106-A=1.2x10-5-因为其中300万人构成针头区域。

  播放段落

  Isolate $\begin{array}{r}A\end{array}$ :
  ::孤立 A :

  播放段落

  $$\begin{array}{rlrl}& A=\frac{1}{3\times {10}^6}\cdot 1.2\times {10}^{-5}& & -rearrangingthetermsgives:\\ & A=\frac{1.2}{3}\cdot \frac{1}{{10}^6}\times {10}^{-5}& & -thenusingthedefinitionofanegativeexponent:\\ & A=\frac{1.2}{3}\cdot {10}^{-6}\times {10}^{-5}& & -evaluate\mathrm{\&}combineexponentsusingtheproductrule:\\ & A=0.4\times {10}^{-11}& & -butweca{n}^{\prime }tleaveouranswerlikethis,so\dots \end{array}$$

  
  ::A=13x106x11.2x10-5-对术语进行重新排列,说明:A=1.231-1106x10-5-然后使用负引号的定义:A=1.2310-6x10-5-评价并结合使用产品规则的引号:A=0.4x10-11-但是我们不能留下这样的答案,所以...

  播放段落

  The area of one bacterium is $\begin{array}{r}4.0\times {10}^{-12}{m}^2\end{array}$ .
  ::一种细菌的面积为4.0×10-12平方米。

  播放段落

  (Notice that we had to move the decimal point over one place to the right, subtracting 1 from the exponent on the 10.)
  :注意我们必须将小数点从一个地方移到右边,从10点的指数中减去1)

  播放段落

  Evaluate Expressions in Scientific Notation Using a Graphing Calculator
  ::使用图形计算计算器评价科学术语中的表达式

  播放段落

  All scientific and graphing calculators can use scientific notation, and it’s very useful to know how.
  ::所有的科学和图形计算计算器都可以使用科学符号,知道如何进行计算非常有用。

  播放段落

  To insert a number in scientific notation, use the [EE] button. This is [2nd] [,] on some TI models.
  ::要在科学符号中插入数字,请使用 [EE] 按钮。对于某些TI模型,这是 [第 2 [ ] 。

  播放段落

  For example, to enter $\begin{array}{r}2.6\times {10}^5\end{array}$ , enter 2.6 [EE] 5. When you hit [ENTER] the calculator displays 2.6E5 if it’s set in Scientific mode, or 260000 if it’s set in Normal mode.
  ::例如,要输入2.6x105,请输入2.6[EE]5. 。如果计算器以科学模式设置,在击中[ENTEER]时显示2.6E5;如果以正常模式设置,则显示260000。

  

  播放段落

  (To change the mode, press the ‘Mode’ key.)
  :要改变模式,请按“模式”键。))

  播放段落

  Using a Calculator 
  ::使用计算器

  播放段落

  Evaluate $\begin{array}{r}(2.3\times {10}^6)\times (4.9\times {10}^{-10})\end{array}$ using a graphing calculator.
  ::使用图形计算器评价 (2.3x106) x(4.9x10-10) 。

  播放段落

  Enter 2.3 [EE] $\begin{array}{r}6\times 4.9\end{array}$ [EE] - 10 and press [ENTER] .
  ::输入2.3[EE]6x4.9[EE]-10并按 [ENTER]。

  

  播放段落

  The calculator displays 6.296296296E16 whether it’s in Normal mode or Scientific mode. That’s because the number is so big that even in Normal mode it won’t fit on the screen. The answer displayed instead isn’t the precisely correct answer; it’s rounded off to 10 significant figures.
  ::计算器显示的是6.296296296E16, 不管是正常模式还是科学模式。这是因为数字太大,即使以正常模式也不适合屏幕上。 所显示的答案不是准确的正确答案,而是四舍五入到10个重要数字。

  播放段落

  Since it’s a repeating decimal , though, we can write it more efficiently and more precisely as $\begin{array}{r}6.\overline{296}\times {10}^{16}\end{array}$ .
  ::由于它是重复的十进制, 我们可以更高效更精确地写作为6.296 1016。

  播放段落

  Example
  ::示例示例示例示例

  播放段落

  Example 1
  ::例1

  播放段落

  Evaluate $\begin{array}{r}(4.5\times {10}^{14}{)}^3\end{array}$ using a graphing calculator.
  ::使用图形计算器进行评价(4.5x10143)。

  播放段落

  Enter (4.5 [EE] $\begin{array}{r}14{)}^{\wedge }3\end{array}$ and press [ENTER] .
  ::输入 (4.5 [EE]14]%3 和按 [ENTER] 。

  

  播放段落

  The calculator displays 9.1125E43. The answer is $\begin{array}{r}9.1125\times {10}^{43}\end{array}$ .
  ::计算器显示为 9.1125E43, 答案是 9.125x1043。

  播放段落

  Review 
  ::回顾

  播放段落

  For questions 1-9, use a calculator to evaluate the expression.
  ::对于问题1-9,使用计算器来评价表达式。

  1. $\begin{array}{r}(3.5\times {10}^4)\cdot (2.2\times {10}^7)\end{array}$
  2. $\begin{array}{r}\frac{2.1\times {10}^9}{3\times {10}^2}\end{array}$
  3. $\begin{array}{r}(3.1\times {10}^{-3})\cdot (1.2\times {10}^{-5})\end{array}$
  4. $\begin{array}{r}\frac{7.4\times {10}^{-5}}{3.7\times {10}^{-2}}\end{array}$
  5. $\begin{array}{r}12,000,000\times 400,000\end{array}$
  6. $\begin{array}{r}3,000,000\times 0.00000000022\end{array}$
  7. $\begin{array}{r}\frac{17,000}{680,000,000}\end{array}$
  8. $\begin{array}{r}\frac{25,000,000}{0.000000005}\end{array}$
  9. $\begin{array}{r}\frac{0.0000000000042}{0.00014}\end{array}$

  播放段落
  10. The moon is approximately a sphere with radius $\begin{array}{r}r=1.08\times {10}^{3}miles\end{array}$ . Use the formula Surface Area $\begin{array}{r}=4\pi r^2\end{array}$ to determine the surface area of the moon, in square miles. Express your answer in scientific notation, rounded to two significant figures.
      ::月亮大约是一个圆球, 半径为 r= 1. 08× 103 英里。 使用公式表层面积 = 4. r2 来确定月球的表面面积, 以平方英里表示。 以科学符号表达您的答复, 四舍五入为两个重要数字 。
  播放段落
  11. The charge on one electron is approximately $\begin{array}{r}1.60\times {10}^{-19}\end{array}$ coulombs. One Faraday is equal to the total charge on $\begin{array}{r}6.02\times {10}^{23}\end{array}$ electrons. What, in coulombs, is the charge on one Faraday?
      ::一种电子的电费大约为1.60×10-19 coulombs, 一种法拉第天等于6.02×1023电子的总电费。在一种电子的电费中,一种法拉第天的电费是多少?
  播放段落
  12. Proxima Centauri, the next closest star to our Sun, is approximately $\begin{array}{r}2.5\times {10}^{13}\end{array}$ miles away. If light from Proxima Centauri takes $\begin{array}{r}3.7\times {10}^4\end{array}$ hours to reach us from there, calculate the speed of light in miles per hour. Express your answer in scientific notation, rounded to 2 significant figures.
      ::离太阳最近的一颗恒星即近半人马半人马,离太阳大约2.5×1013英里。如果近半人马半人马的光线需要3.7×104小时才能到达我们,请以每小时英里计算光速。以科学符号表达您的回答,四舍五入到两个重要数字。

  播放段落

  Review (Answers)
  ::回顾(答复)

  播放段落

  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。