| Contents for this page | Related topics |  |
| What is scientific notation? Converting a number to scientific notation Additional questions |
Dimensions Units and Measurements Significant figures |
 Data |
| Learning Outcomes | ||
| After studying this section, you will be able to express numbers in exponential (scientific) notation. | ||
Scientists have a need to express very large (or very small numbers) in some convenient way. For example, astronomers measure the distance to stars in LIGHT YEARS, a unit of distance whichconveniently expresses the huge distances that are involved. A light year is the distance which light travels in one year. Let us see how many metres there are in one light year. Light travels at a speed of 300000000 m/s (three hundred million metres per second).
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This number is very inconvenient to read and to write. Even if we tidy it up to read: 9 460 800 000 000 000 m, it is very easy to make a mistake. |
The solution to this problem is to write such very large (or very small) numbers in SCIENTIFIC NOTATION.
| Scientific notation involves writing a number as the product of two numbers. The first one, the DIGIT VALUE, is always more than one and less than 10. The other, the EXPONENTIAL TERM, is expressed as a power of 10. |  |
Computers normally have problems displaying the exponential term. So, one can also write a number in scientific notation in the following way:
9.4608E15 (or 9.4608e15) stands for 9.4608 x 1015 (numerical size of one light year)
3.7E-11 (or 3.7e-11) stands for 3.7 X 10-11 (numerical size of the hydrogen atom).
In the numerical problems that are set in the Electronic Science Tutor®, use the above format for large or small numbers.
To convert a large number to scientific notation, divide the number by 10 as many times as is needed to get a digit value less than 10 and greater than 1. Multiply this digit value by an exponential term where the exponent is the number of times that you have divided by 10. In the example on the right, the number 1230000000, expressed in scientific notation becomes 1.23 x 109.
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To convert a small number to scientific notation, multiply the number by 10 as many times as is needed to get a digit value greater than 1 and less than 10. Multiply this digit value by an exponential term where the exponent is the negative number of times you have multiplied by 10.
In the example on the left, the number 0.0000000123, expressed in scientific notation, becomes 1.23 x 10-8. |
Glossary