9.6 科学标签和选择合理合理单位中的比较数字-interactive

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• 选择节科学标签和选择合理合理单位中的比较数字

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  科学标签和选择合理合理单位中的比较数字

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  Comparisons in Science
  ::科学比较

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  Comparing objects helps to understand them. Astronomers measure distances of stars to help understand their location relative to Earth so that the stars can be mapped. In medicine, cell sizes are compared to determine whether or not cells are healthy. Working in one of these fields will all but guarantee that you will have to compare numbers in scientific notation.
  ::比较对象有助于理解它们。天文学家测量恒星的距离,以帮助了解它们相对于地球的位置,从而可以绘制恒星。在医学上,细胞大小被比较以确定细胞是否健康。在其中一个领域工作只能保证在科学符号中比较数字。

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  Discussion Question
  ::讨论问题

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  Rob is an astronomer and was looking at the stars. He found one star which was  $\begin{array}{r}9.7\times {10}^{12}\end{array}$ miles away while another star was  $\begin{array}{r}4.7\times {10}^{15}\end{array}$  miles away. He wanted to know which star was further away. Without rewriting the numbers in standard form, which star do you think is further away? Discuss your thoughts in class or  with your classmates.
  ::Rob是天文学家,当时正在看星星。他发现一颗恒星在9.7×1012英里之外,而另一颗恒星在4.7×1015英里之外。他想知道哪个恒星离地球更远。他不把数字改写成标准格式,你认为哪个恒星离地球更远?在课堂上或与同学讨论你的想法。

   

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  Comparing Big Numbers
  ::比较大数字

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  To compare numbers in scientific notation you will need to use the following steps:
  ::为了比较科学符号中的数字,您需要使用以下步骤:

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  1. Compare the .
     ::比较一下
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  2. If the exponents are the same compare the coefficients.
     ::如果指数相同,则比较系数。

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  You will need to compare the exponents first because the exponent represents place value .
  ::您需要先比较指数, 因为指数代表了位置值 。

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  • The number  $\begin{array}{r}9.7\times {10}^{12}\end{array}$  is equivalent to 9,700,000,000,000.
    ::数字9.7×1012等于9 700 000 000 000。
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  • The number  $\begin{array}{r}4.7\times {10}^{15}\end{array}$  is equivalent to 4,700,000,000,000,000.
    ::这个数字4.7×1015相当于4 700 000 000 000 000美元。

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  It does not matter how large the coefficient is if the one exponent is larger than the other because this means that one place value is larger than the other. If the exponents are the same, then the numbers have the same place value. In this case, you would have to compare the coefficients with the greater coefficient representing the greater number.
  ::如果一个指数大于另一个指数,则该系数有多大并不重要,因为这意味着一个位置值大于另一个位置值。 如果指数相同,那么数字具有相同的位置值。 在这种情况下,您需要将系数与代表更多数量的更大系数进行比较。

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  Discussion Question  
  ::讨论问题

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  If two exponents are the same, why would the coefficient tell us which number is greater?
  ::如果两个指数相同,为什么系数告诉我们哪个数字更大?

   

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  Comparing Really Small Numbers
  ::比较真正小数字

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  The average healthy red blood cell measures at around $\begin{array}{r}8\times {10}^{-6}\end{array}$  meters in diameter. If a red blood cell has a significantly larger diameter, it could signal that the patient has an illness. Mikaela is a doctor who was checking the red blood cells of a patient. She measured a red blood cell with a diameter of $\begin{array}{r}1.01\times {10}^{-7}\end{array}$  meters in diameter. Is this cell larger or smaller than average? To determine this she will use the same approach that you used with large numbers.
  ::平均健康红血细胞直径约8x10-6米。如果红血细胞直径大得多,它可以表示病人有病。Mikaela是检查病人红血细胞的医生,直径为1.01×10-7米。这个红血细胞大于或小于平均。为了确定这一点,她将使用与大量病人相同的方法。

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  1. Compare the exponents.
     ::比较指数 。
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  2. If the exponents are the same compare the coefficients.
     ::如果指数相同,则比较系数。

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  When you compare the exponents -6 and -7 you can see that -6 is greater than -7. This means that $\begin{array}{r}8\times {10}^{-6}\end{array}$  is greater than $\begin{array}{r}1.01\times {10}^{-7}\end{array}$ . The cell with a diameter of $\begin{array}{r}1.01\times {10}^{-7}\end{array}$ meters is smaller than average and is likely a healthy cell.
  ::当比较指数 -6 和 -7 时,可以看到 -6 大于 -7.,这意味着 8×10-6 大于 1.01×10-7 。直径为 1.01×10-7 公尺的细胞小于平均数,而且很可能是健康的细胞。

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  Mikaela measured another red blood cell and found the diameter to be $\begin{array}{r}9\times {10}^{-6}\end{array}$  meters. Is this cell larger or smaller than the average red blood cell with a diameter of $\begin{array}{r}8\times {10}^{-6}\end{array}$ ? If you compare the exponents you find that they are equal. However, 9 is greater than 8 so $\begin{array}{r}9\times {10}^{-6}\end{array}$  is greater than $\begin{array}{r}8\times {10}^{-6}\end{array}$ . This means that the cell with a diameter of $\begin{array}{r}9\times {10}^{-6}\end{array}$ meters is larger than normal and could potentially be unhealthy. In this case, Mikaela would likely look at more red blood cells to see if the diameter is a trend or an outlier.
  ::Mikaela测量了另一个红血细胞,发现直径为9×10-6米。 这个细胞大于还是小于平均红血细胞,直径为8×10-6米。 如果比较一下你发现相等的指数, 但是, 9 大于 8 so 9×10-6 大于 8×10-6 等于 8×10-6 。 这意味着直径为 9×10-6米的细胞大于正常, 并且可能不健康。 在这种情况下, Mikaela 可能会看到更多的红血细胞, 以观察直径是趋势还是外值 。

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  Why is it enough to compare exponents if they are not equal?
  ::如果指数不相等,为什么仅仅比较指数就足够了?

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  While meters are the generally accepted unit for distance in science, telling someone that a cell is  $\begin{array}{r}9\times {10}^{-6}\end{array}$  meters long can be difficult to interpret. Use the interactive below to choose a more appropriate unit.
  ::虽然米是科学中一般接受的距离单位, 但告诉某人一个9x10-6米长的细胞可能难以解释。 使用下面的交互功能选择一个更合适的单位 。

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  Which unit do you think would be more appropriate than the meter? Why?  
  ::你觉得哪个单位比仪表更合适?

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  Comparing Numbers in Different Forms
  ::以不同形式比较数字

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  To compare numbers from different forms you will need to convert them to the same form. It generally does not matter whether you choose to convert the numbers to or standard form. Choose the option that you feel makes the most sense, is easiest, and fits the situation best.
  ::要比较不同表格的数字, 您需要将其转换为相同格式。 通常, 您选择将数字转换为或标准格式并不重要。 选择您认为最合理、 最简单、 最符合情况的选项 。

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  Example
  ::示例示例示例示例

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  Which is greater: $\begin{array}{r}4.26\times {10}^{10}\end{array}$  or 4,260,000,000?
  ::哪一个更大:4.26×1010或4,260,000,000?

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  T o compare these numbers, convert 4,260,000,000 into scientific notation. You will have to move the decimal 9 places to the left giving you  $\begin{array}{r}4.26\times {10}^9\end{array}$ . You can now answer the question using the steps you learned in the previous activities.
  ::要比较这些数字, 请将 4 260,000,000 转换为科学符号。 您需要将小数点 9 位移到左边, 给您带来 4. 26 x 109 。 现在您可以使用您在先前活动中学到的步骤回答问题 。

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  Which is greater: $\begin{array}{r}4.26\times {10}^{10}\end{array}$  or $\begin{array}{r}4.26\times {10}^9\end{array}$ ?
  ::哪一个更大:4.26×1010或4.26×109?

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  1. Compare the exponents.
     ::比较指数 。
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  2. If the exponents are the same compare the coefficients.
     ::如果指数相同,则比较系数。

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  If you compare the exponents, 10 is greater than 9 so  $\begin{array}{r}4.26\times {10}^{10}\end{array}$  is greater than $\begin{array}{r}4.26\times {10}^9\end{array}$ .
  ::如果比较指数,10大于9,4.26×1010大于4.26×109。

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  See the interactive below to practice ordering numbers in both standard form and scientific notation. 
  ::以标准格式和科学符号两种方式练习顺序编号,见下文互动。

   

   

   

   

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  Different units can be used for very large or very small measurements.  Use the interactive to explore the best units for various lengths and areas and answer the questions below.
  ::不同的单位可用于非常大或非常小的测量。 使用互动来探索不同长度和地区的最佳单位, 并回答下面的问题 。

   

   

   

  Summary

  播放段落 When comparing number written in scientific notation: 播放段落 Start by comparing the exponents ::从比较指数开始 播放段落 If the exponents are the same compare the coefficients ::如果指数是相同的,比较系数 ::比较以科学符号书写的数字时:先比较指数,如果指数相同,则比较系数。 播放段落 When comparing a number in standard form to a number in scientific notation, convert the number in standard form to scientific notation. ::在将标准格式的数字与科学符号中的数字进行比较时,将标准格式的数字转换为科学符号。