Scientific notation math is a form of presenting very large numbers or very small numbers in a simpler form. As we know, whole numbers can be extended to infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.
The exponent must be a non-zero integer, which means it can be either positive or negative.
The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10.
Coefficients can be positive or negative numbers including whole and decimal numbers.
The mantissa carries the rest of the significant digits of the number.
When the scientific notation of any large numbers is expressed, then we use positive exponents for base 10.
When the scientific notation of any small numbers is expressed, then we use negative exponents for base 10.
Scientific Notation Example
Scientific notation problemsinclude questions like below given examples.
1.Convert 0.00000046 into scientific notation.
ØMove the decimal point to the right of 0.00000046 up to 7 places.
ØThe decimal point was moved 7 places to the right to form the number 4.6.
ØSince the numbers are less than 10 and the decimal is moved to the right. Hence, we use a negative exponent here.
Ø ⇒ 0.00000046 = 4.6 × 10-7
2.Convert 301000000 into scientific notation.
ØMove the decimal to the left 8 places so it is positioned to the right of the leftmost non-zero digit 3.01000000.
ØRemove all the zeroes and multiply the number by 10.
ØNow the number has become = 3.01.
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The primary reason why scientific notation is important is that it allows us to convert very large or very small numbers into much more manageable sizes. When these numbers are in scientific notation, it is much easier to work with them.
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