9.5 科学符号中的写作数字-interactive

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• 选择节科学标注中的写作编号

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  科学标注中的写作编号

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  Scientific Notation
  ::科学符号

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  The lesson  discussed  how astronomers study some of the some of the furthest distances in the universe  and how biologists and nanotechnology engineers study some of the smallest objects. In this lesson, you will learn the notation they use to write the small and large numbers that they measure.  is a format that expresses a number as a value between 1 and 10 multiplied by a power of ten.  The format for scientific notation appears like this:
  ::该课程讨论了天文学家如何研究宇宙中一些最遥远的距离,生物学家和纳米技术工程师如何研究一些最小的天体。在这个课程中,你将学习他们用来写他们测量的大小数字的符号。这是一个表示数字值为1至10乘以10的乘以10的公式格式。科学符号格式如下:

  

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  Using scientific notation, the number 300 can be written as $\begin{align*}3 \times {10}^{2}\end{align*}$  which means $\begin{align*}3\times 100.\end{align*}$  The 100 is written as a power of ten. The number 0.07 can be written as  $\begin{align*}7 \times {10}^{-2}\end{align*}$  which means  $\begin{align*}7 \times \frac{1}{100}\end{align*}$ . Recall that  $\begin{align*}{10}^{-2}\end{align*}$  can be written as  $\begin{align*}\frac{1}{10 \cdot 10}\end{align*}$   or $\begin{align*}\frac{1}{100}\end{align*}$ . 
  ::使用科学标记,300号可以写为3x102,这意味着 3x100。100号可以写为10的功率。0.07号可以写为7x10-2,这意味着 7x100。请注意,10-2号可以写为110x10或1100。

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  This notation is useful for writing particularly large or small numbers. A number as large as 45,300,000,000 or as small as 0.00000000048 would be difficult to write without scientific notation. Take a look at some of the tricks that scientists use to convert numbers to scientific notation.
  ::这个标记对于写出特别大或小的数字非常有用。 多达45,300,000,000,000,48 或小到000,000,000,000,000,000,000,000,48 在没有科学标记的情况下很难写出。 看一下科学家用来将数字转换为科学标记的一些技巧。

    

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  Writing Large Numbers in Scientific Notation
  ::在科学符号中写入大数

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  Astronomers use telescopic lenses to see the nearest planets, stars and other cosmic bodies. For example, the closest star to Earth is approximately 25,700,000,000,000 miles away. Given that this is the closest star, this should give you an idea of the scale on which that astronomers operate. How would you write this number using scientific notation?
  ::天文学家使用遥视镜观察最近的行星、 恒星和其他宇宙体。 例如, 离地球最近的恒星大约在25,700,000,000英里之外。 鉴于这是最接近的恒星, 这应该能让您了解天文学家的运行规模。 您如何使用科学符号写入这个数字 ?

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  Example
  ::示例示例示例示例

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  Write 25,700,000,000,000 in scientific notation.
  ::写25,700,000,000 在科学标记。

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  Use  these  steps to write the number 25,700,000,000,000 in scientific notation.
  ::使用这些步骤,在科学符号中写出25 700 000 000 000美元。

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  1. Move the decimal point to the right of the first non- zero digit so that you have a number between 1 and 10.
     ::将小数点移到第一个非零位数右侧,以便数字在1到10之间。

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  The first non-zero number is 2. If you slide the decimal point from the end of the number to the right of the 2, you will get 2.5700000000000. You don’t need the extra zeroes and can write this as 2.57. The number 2.57 is between 1 and 10 as you wanted.
  ::第一个非零数字是2。如果将小数点从数字的末尾滑到2的右侧,您将得到2.57000000000。您不需要额外的零位,可以写为2.57。数字2.57是1到10之间。

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  2. Multiply by 10 to the power of the number of places the decimal moved. 
     ::乘以 10 到十进制移动位数位数的功率。

  

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  Here, you had to move the decimal 13 places to the left so the answer will be $\begin{align*}2.57 \times {10}^{13}.\end{align*}$
  ::在这里,你不得不将小数点13 位移到左边,所以答案将是2.57×1013。

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  If you multiply 2.57 by 10 thirteen times, you will get back to the original number. Powers of ten work so well because multiplying by ten moves the decimal one place to the right without changing any of the digits.
  ::如果乘以 2.57 乘以 10 13 乘以 10 13 倍,您就会回到原数。 10 功率非常好, 因为乘以 10 将小数点之一移到右边, 而不改变任何位数 。

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  Use the interactive below to practice writing large numbers in scientific notation.  
  ::用下面的交互式文字练习在科学符号中写出大量数字。

   

   

   

   

   

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  Writing Small Numbers in Scientific Notation
  ::在科学标签中写小数

  

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  Biologists use microscopic lenses to view cells, bacteria, and many other organisms. The image above shows an alloy made of the strontium and titanium atoms. The size of one atom is approximately 0.0000000005 meters long. To write a small number in scientific notation, you will follow a similar strategy to the one used to write a big number.
  ::生物学家使用显微镜查看细胞、细菌和许多其他生物。 上面的图像显示了由和钛原子制成的合金。 一个原子的大小约为 0000000005 公尺。 要在科学符号中写下少量数字, 您将遵循与用来写大数字的策略相似的策略 。

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  Example
  ::示例示例示例示例

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  Write 0.0000000005 in scientific notation.
  ::写50000005 在科学标记。

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  1. Move the decimal point to the right of the first non-zero digit so that you have a number between 1 and 10.
     ::将小数点移到第一个非零位数右侧,以便数字在1到10之间。

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  The first non-zero digit is 5, so you should move the decimal to the right of the 5 to get 5 which is a number between 1 and 10.
  ::第一个非零位数为 5, 所以您应该将小数点移到 5 点右侧, 才能得到 5 点, 这个数字在 1 点到 10 点之间。

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  2. Multiply that by 10 to the power of the negative number of places the decimal moved.
     ::乘以乘以 10 到负数的功率, 乘以小数点移动后的负数 。

  

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  Y ou had to move the decimal 10 places to the right so the answer  is   $\begin{align*}5 \times {10}^{-10}.\end{align*}$
  ::您必须将小数十位移到右边, 答案是 5x10- 10 。

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  If you divided 5 by 10 ten times, you would get back to the original number. This notation works so well with powers of ten because dividing by ten moves the decimal one place to the left without changing any of the digits.
  ::如果您除以 5 乘以 10 十 次, 您就会回到原来的数字。 这个符号非常有效, 具有十倍的功率, 因为除以 10 将小数点移到左边, 不改变任何位数 。

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  Use the interactive below to practice writing small numbers in scientific notation. 
  ::用下面的交互式文字练习在科学符号中写少量数字。

   

   

   

   

   

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  LARS Helps to Remember the Rules
  ::劳改会帮助人们记住规则

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  The rules for writing large numbers and small numbers in scientific notation are so similar because they are the same rules. The only difference depends on the way that you move the decimal. If you are moving the decimal to the left, then you add the number of places the decimal moved to the exponent. If you are moving the decimal to the right, then you subtract the number of places the decimal moved to the exponent. To remember this all you have to remember is four letters:
  ::在科学符号中写出大数和小数的规则非常相似,因为它们是相同的规则。唯一的区别取决于您移动小数点的方式。如果将小数点移到左边,那么将增加小数点移到指数点的位数。如果将小数点移到右边,那么将减去小数点移到指数点的位数。要记住这一点,只需记住四个字母:

  

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  Write the number 5,900 in scientific notation.
  ::在科学符号中写5900号

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  To write this number in scientific notation, you must first move the decimal 3 places from the end of the number to between the 5 and the 9. Since you are moving the decimal 3 places to the left, you will add to the exponent. There is no exponent to add it to so you will add it to zero. Every number in standard form can secretly be written as being multiplied by $\begin{align*}{10}^{0}\end{align*}$  because $\begin{align*}10^0\end{align*}$  means 1. The answer is  $\begin{align*}5.9 \times {10}^{3}\end{align*}$ .
  ::要在科学符号中写入此数字, 您必须先将小数小数三位数从数字的末尾移到5和9之间。 由于您正在将小数三位数移到左边, 您将添加到指数中。 没有要添加的提示可以将其添加到零 。 标准格式中的每个数字都可以以100乘以100, 因为 100 表示 1 。 答案是 5. 9x103 。

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  Example
  ::示例示例示例示例

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  Write the number 0.00042 in scientific notation.
  ::在科学符号中写下0.00042号号码。

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  To write this number in scientific notation, you must first move the decimal 4 places from where it is in the original number to between the 4 and the 2. Since you are moving the decimal 4 places to the right, you will subtract from the exponent. Again, because there is no exponent to subtract from, use the exponent 0. The answer is $\begin{align*}4.2 \times {10}^{-4}\end{align*}$ .
  ::要在科学符号中写入此数字, 您必须先将小数点 4 移到 4 和 2 之间。 由于您正在将小数点 4 移到右边, 您将从引号中减去。 另外, 因为没有要从中减去的引号, 请使用 exponent 0。 答案是4.2x10- 4 。

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  Use the interactive below to explore how moving the decimal left or right affects the decimal.  
  ::使用下面的交互数据来探索小数点左右的移动如何影响小数点。

   

   

   

   

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. Move the decimal between the digits 1 and the 2. If you were to move the decimal one place more to the left what would happen to the exponent?
     ::将小数位数移到两位数字之间。 如果您要把小数位数移到左边, 那么引言人会发生什么?
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  2. Is this true no matter the starting point? How do you know?
     ::这是否属实 不论起点如何 你怎么知道的
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  3. Move the decimal back to between the digits 1 and the 2. If you were to move the decimal one place to the right what would happen to the exponent?
     ::将小数点后移到两位数字之间。 如果您要将小数点后移到右侧, 那么引言人会发生什么 ?
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  4. Is this true no matter the starting point? How do you know?
     ::这是否属实 不论起点如何 你怎么知道的

   

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  Converting Back to Standard Form
  ::转换回标准表格

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  When a scientist looks at a number in scientific notation, they need to understand what it is is in standard form. To do this, they have to move the decimal the same number of places it took to become scientific notation in the opposite direction. A positive exponent means to move the decimal to the right because you are repeatedly. A negative exponent means to move the decimal to the left because you are repeatedly. A simple trick for direction is that a positive exponent should result in a big number (greater than 1). A negative exponent should result in a small number (less than 1). Use the interactive below to practice converting the following numbers into scientific notation.
  ::当科学家在科学符号中看到数字时,他们需要理解什么是标准格式。要做到这一点,他们必须把小数点与在相反方向上成为科学符号时所用的小数点相同。正缩略语表示将小数点向右移动,因为您反复出现。负缩略语表示将小数点向左移动,因为您反复出现。方向上的一个简单技巧是,正缩略语应导致一个大数字(大于1),负缩略语应导致一个小数字(少于1),使用下面的交互方式将以下数字转换为科学符号。

   

  Summary

  播放段落 Numbers written in scientific notation are in the form of a coefficient multiplied by 10 to a positive or negative power. For example:  $\begin{align*}1.2\times10^{-3}\end{align*}$   ::以科学符号书写的数字以系数乘以10乘以正或负功率的形式出现。例如:1.2×10-3。 播放段落 When writing numbers in scientific notation: 播放段落 If the decimal is moved to the left, add the number of places the decimal moved to the exponent. ::如果小数点被移到左边,请加上小数点被移到指数的位数。 播放段落 If the decimal is moved to the right, subtract the number of place the decimal moved to the exponent. ::如果将小数点移到右边,请减去小数点移到引言处的位数。 ::当在科学符号中写入数字时:如果小数点移到左边,请加上小数点移到表列处的位数。如果小数点移到右边,请减去小数点移到表列处的位数。