# 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.

A number expressed in scientific notation - http://www.tutornext.com/math/scientific-notation.html is based on powers of 10. If n is a positive integer, then the mantissa of the scientific notation is multiplied by n factors of 10. If n is a negative integer, then the mantissa of the scientific notation is divided by n factors of 10.

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

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