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
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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