Measurements in science are often of very tiny amounts (like the radius of an atom) or very large amounts (like the radius of the Earth's orbit). These numbers can be represented in several ways. One way is to use measuring units that are about the correct size. In thatcase, the radius of the neon atom is about 0.000 000 000 035 meters, and the radius of the Earth's orbit is about 150 000 000 000 meters. This at least lets you compare the two numbers, but it's still not a very convenient way to write them. The solution to that is to use scientific notation. In scientific notation, the significant digits are always all shown, with the decimal point after the first one. This number is shown multiplied by 10 raised to the appropriate power to give the number the correct value. For the radius of the Earth's orbit, this would be 1.5x1011 m. For a number smaller than one, the exponent is a negative number, to show that the significant part of the number is divided by 10 a certain number of times. The radius of a neon atom is therefore written as 3.5x10-11 m.
To change the appearance of a number that is in scientific notation to floating point notation ("normal numbers"), use the following rules:
To change the appearance of a number that is in scientific notation to floating point notation ("normal numbers"), use the following rules:
- If the exponent is positive, move the decimal place to the right that many times. Add zeroes if necessary, but if you do remember not to write the decimal point.
- If the exponent is negative, move the decimal place to the left that many times. Add zeroes if necessary, but make sure you do write the decimal point.
scientificnotation.pdf | |
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scientificnotation1.pdf | |
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scientificnotation2.pdf | |
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scientificnotationandorderofoperations.pdf | |
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