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# Math Examples of Scientific Notation and Rational Numbers

• ## 0.0035 times 10 to the power of negative 2 in scientific notation?

Scientific Notations are generally used to represent the Numbers in mathematics that seem to be very insignificant or very big. This type of number will possess just 2 factors out which first one appears in between numbers 1 and 10. Second factor is usually written in form of an exponent of 10. For example, 1012 means exponent of 10 is 12. This is what we call as scientific representation of any number. We are calling two numbers as factors because numbers that are multiplied to each other to get a product are called as factors only.

Let us consider an example to understand the concept of converting any number into its scientific form: We have to represent 0 Point 0035 times 10 to the power of negative 2 in scientific notation. Remember first factor has to lie between 1 and 10. This makes necessary for us to keep on shifting the decimal point until we get a digit lying between 1 and 10. Here, in our example the number is 0.0035. We can see that digit that lies between 1 and 10 is lying to the right of decimal at thousands place. So, at least 3 times the decimal point has to be shifted to get desired factor. That is we have to multiply 0.0035 by 103 to get 3 in the units place to the left side of decimal. We get:
0.0035 * 103 / 103 = 3.5 * 10-3,
Also number has to be multiplied by 10-2 and then final scientific notation will be decided. On multiplying 10-2 by 3.5 * 10-3, we get following result:
3.5 * 10- (3 + 2) = 3.5 * 10-5,
So, second factor is 10-5 and scientific notation for desired number is given as:
3.5 * 10-5.
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