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Explain Scientific Notation method of measurement. |
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Answer» A chemist has to deal with numbers as large as 602, 200, 000, 000, 000, 000, 000, 000 for the molecules of 2 g of hydrogengas or as small as 0.00000000000000000000000166 g mass of a H atom. SIMILARLY other constants such as Planck.s constant, speed of light, charges on particles etc., involve numbers of the above magnitude. This problem is SOLVED by using scientific notation for such numbers, i.e., exponential notation in which any number can be represented in the form `Nxx10^(n)` where n is an exponent having positive or negative VALUES and N is a number ( called digit term) which VARIES between 1.000... and 9.999... e.g. : we can write 232.508 as `2.32508 xx 10^(2)` in scientific notation. Similarly, 0.00016 can be written as `1.6xx10^(-4)`. Multiplication and Division : These two operation follow the same rules which are there for exponential numbers. e.g. :1 `(5.6xx10^(5))xx(6.9xx10^(8))=(5.6xx6.9)(10^(5)+8)` `=(5.6xx6.9) xx10^(13)` `=38.64xx10^(13)` `3.864xx10^(14)` e.g.: 2 `(2.7xx10^(-3))/(5.5xx10^(-4))=(2.7 div 5.4)(10^(-3 -4))` `=4.909xx10^(-8)` Addition and substraction : For these two operations, first the numbers are written in such a way that they have same exponent. e.g. : Adding `6.65xx10^(4)` and `8.95xx10^(3), 6.65xx10^(4)+0.895xx10^(4)` exponent is made same for both the number. Then, these number can be added as follows, `(6.65+0.895) xx10^(4)=7.545xx10^(4)` Similarly,the substraction of two numbers can be done as shown below. `2.5xx10^(-2)-4.8xx10^(-3)=(2.5xx10^(-2))-(0.48xx10^(-2))` `=(2.5-0.48)xx10^(-2)` `=2.02xx10^(-2)` |
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