Scientific notation
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Scientific notation is used to express very large numbers and very small numbers in standard form/ scientific-notation using exponents.Scientific-notation is just a short hand way of expressing gigantic numbers like 615,000,000 or incredibly small numbers like 0.0000000000118. This method is used by engineers, mathematicians, scientists.
The study of exponents help us to express very large number such as 6,000,000,000 which is 6 x 10 ^{9} and small numbers such as 0.000,000,006 as (6)/ 1,000,000,000 = 6 x 10 ^{-9}
• 1.2 ×10 ^{14} -> the positive exponent indicates a large number.
• 7.89 × 10 ^{-21} - > the negative exponent indicates a small number.
Note : The scientific numbers always lies between 0 and 10
( 0< number < 10)
Scientific Notation | Standard Form |
4.23 ×10^{2} | 423 |
4.23 × 10^{3} | 4,230 |
4.23 ×10^{4} | 42,300 |
4.23 ×10^{5} | 423,000 |
4.23 ×10^{6} | 4,230,000 |
Conversion of number into scientific- notation
Write the following in scientific-notation :
1) 418500
As there is no decimal so consider the decimal after the number
= 418500 .
The decimal will shift 5 places to left, so the exponent of 10 is positive.
<
= 4.18 x 10 ^{5}
2) 26000000000
= 2.6 x 10 ^{10} [ decimal will shift 10 places to left]
3) 0.0000056
As there is decimal
The decimal will shift 6 places to right, so the exponent of 10 is negative.
<
= 5.6 x 10 ^{-6}
4) 0.0000826
= 8.26 x 10 ^{-5}
5) 0.0000012 x 2500000000
Write each number in scientific-notation
0.0000012 = 1.2 x 10 ^{-6}
2500000000 = 2.5 x 10 ^{9}
So, 0.0000012 x 2500000000 =(1.2 x 10 ^{-6} )x(2.5 x 10 ^{9}
= 3 x 10 ^{-6+ 9}
= 3 x 10 ^{3}
= 3000
Conversion of Scientific form to standard form
Exponents
• Laws of Exponents
• Rational Exponents
• Integral Exponents
• Scientific notation
• Solved examples on Scientific-Notation
• Solved Examples on Exponents
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