1.29 科学说明
章节大纲
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Most of the stars pictured in this view of the night sky are hundreds of light years from Earth. A light year is the that light can travel in a year, or about 6 trillion (6,000,000,000,000) miles. As this example shows, quantities in science may be very large. Many other quantities in science are very small. Both very large and very small numbers have many zeroes, so they are hard to read and write without making mistakes. That’s where scientific notation comes in.
::在夜空的这种景象中描绘的多数恒星都是几百光年,距离地球数百光年。光年是光能在一年中行走,大约6万亿美元(6 000 000 000 000)英里。正如这个例子所显示的那样,科学的数量可能非常大。其他许多科学数量都非常小。非常大和非常小的数量都有许多零,因此它们很难读写,而不会犯错误。这就是科学符号出现的地方。What Is Scientific Notation?
::什么是科学符号?Scientific notation is a way of writing very large or very small numbers that uses exponents. Numbers are written in this format:
::科学标记是一种使用引号写出非常大或非常小的数字的方式。
::a×10bThe letter a stands for a decimal number, and the letter b stands for an exponent, or power, of 10. For example, the number 300 is written in scientific notation as 3.0 × 10 2 . The number 0.03 is written as 3.0 × 10 -2 .
::字母 a 表示小数数,字母 b 表示10的指数或功率。 例如,300 以科学符号书写为 3.0 × 102. 。 0. 03 表示为 3.0 × 10-2 。Using Scientific Notation
::使用科学名词It’s easier to convert numbers to and from scientific notation than you might think. Refer to the examples on the chalkboard in the Figure as you read the following steps. Follow the steps in the sequence listed here to convert a number to scientific notation. Follow the steps in the reverse order to convert a number from scientific notation.
::将数字转换成科学符号比你想的要容易得多。 当您读取以下步骤时, 请参考图中黑板上的例子。 跟随在此列出的序列步骤将数字转换为科学符号。 跟随倒序步骤将科学符号中的数字转换为数字。 跟随倒序步骤将科学符号中的数字转换为数字。-
Move the decimal point left or right until you reach the last nonzero digit. This new decimal number is
a
in
a
× 10
b
.
::将小数点向左移动或向右移动,直到您达到最后一个非零位数。这个新的小数点数是 x 10b 中的a。 -
Count how many places you moved the decimal point in Step 1. This number is
b
in
a
× 10
b
.
::计算您移动第1步小数点时的位数。 这个数字是 b 乘以 a × 10b 。 -
Did you move the decimal point left (first example in the
Figure
)? If so,
b
is positive. Did you move the decimal point right (second example in the
Figure
)? If so,
b
is negative.
::您是否向左移动小数点(图中的第一个示例) ? 如果是, b 是正数。 您是否向右移动小数点(图中第二个示例) ? 如果是, b 是负数 。
These two examples show how to convert large and small numbers to scientific notation. Q: Apply the steps above to write 450,000 in scientific notation.
::问题:应用上述步骤在科学符号中写45万张。A: The unwritten decimal point in this number follows the last zero. Move the decimal point from this position to the left and stop just before the last digit, giving you 4.5 for a . The decimal point was moved five places to the left, so b is 5. In scientific notation the number is 4.5 × 10 5 .
::A: 这个数字中的未写小数点在最后一个零之后。 将小数点从此位置移到左边, 并在最后一个数字之前停止, 给您4.5 表示一个数字。 小数点向左移动了五个位数, 所以b是 5 。 在科学符号中, 数字是4.5 x 105。Q: Apply the steps in reverse order to write the number that is expressed as 7.2 × 10 4 in scientific notation.
::问题:应用倒数步骤,在科学符号中以7.2×104表示编号。A: Add zeroes to 7.2 as you move the decimal point four places to the right. This gives you the number 72,000.
::A: 当向右移小数点四位时, 向右移时, 向7.2 加零 。 这给了您72,000 个数字 。Summary
::摘要-
Scientific notation is a way of writing very large or very small numbers that uses exponents. Numbers are written in the format
a
× 10
b
.
::科学标记是一种写出非常大或非常小的数字的方法,它使用引号。数字以 a × 10b 格式写成。 -
Changing numbers to or from scientific notation is easy to do by following three simple steps.
::通过遵循三个简单的步骤,从数字到科学标记或从数字到科学标记的改变是很容易做到的。
Review
::回顾-
What is scientific notation? Why are numbers written in scientific notation?
::什么是科学符号?为什么数字写在科学符号中? -
Write 0.0045 in scientific notation.
::写0.0045 在科学符号。 -
What number is written as 6.0 × 10
6
in scientific notation?
::科学符号中的编号是 6.0 × 106?
-
Move the decimal point left or right until you reach the last nonzero digit. This new decimal number is
a
in
a
× 10
b
.
