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Showing posts with label scientific notation rules. Show all posts
Showing posts with label scientific notation rules. Show all posts

Wednesday, June 20, 2012

Scientific notation :word problem and expanded form


We come across large numbers in our day  to day life .we can express large number conveniently expressed using exponents.every large number can be expressed as k x 10n , where k is some natural number .however , for the sake of uniformity , we write the number in the form k x 10n  where k is terminating decimal number greater than or equal to 1 and less than 10 and n is a natural number .To  express large number into standard form is scientific notation.
Scientific notation rules
1) For the positive number , move the decimal  point to the left to bring non-zero digit to the left of the decimal point .
Example of scientific notation  :To express 41460. 5 in the standard form of decimal , we have to move decimal point 4 places on the left to get 4.14605 , so 41460.5 in the standard form of decimal is 4.14605 x 104.
2) If the given number is less  than one , then move the decimal point to the right to obtain one non –zero  digit  to the left  of the decimal point. If the decimal point is moved p places to the right ,then multiply the new number by 10^-n to express the given number in the standard form of decimal
Example of scientific notation  : To Express 0.03453 in the standard form of decimal we will have to move the decimal poit 2 places on the right to get 3.453 .so , 0.03453 in the standard form of decimal  is 3.453 x 10^-2
Scientific notation word problems
Example 1: A lake covers an area of about 3.5*10^5 square feet and its average depth of lake  is about 16 feet.   Calculate  the cubic feet of water in the lake.
Solution1) Volume  of lake =  area x depth
                                             =  3.5 *10^5 x 16 cubic feet
                                            = 56 *10^5 cubicfeet
                                           = 5.6 x 10^6 cubic feet
Expanded form : The expanded  form of a number can also be expressed  in term of powers of 10 by using
10^0 = 1 , 10^1 = 10 , 10^2 = 100
Example of expanded form :
1) 6467 = 6 x1000+ 4 x 100+ 6 x10 + 7
2) 7465267= 7 x 1000000+ 4 x100000+6x10000+5x1000+2x100+6x10+7
                               = 7x10^6+4x10^5+6x10^4+x10^3+2x10^2+6x10^1+7x10^0